Method to determine pixon map in iterative image reconstruction and spectral analysis

FIELD: physics, computer engineering.

SUBSTANCE: invention relates to means of reconstructing a surveillance object on an image. The method comprises creating an object model in space, converting the object model from object space into a data space to obtain a data model, selecting a merit function to determine approximation of the data model, determining an updating variable of the object model, smoothing the updating variable via convolution thereof using each pixon kernel, selecting for each point of the input object a pixon kernel having the greatest size and which corresponds to a predetermined minimum criterion, generating a pixon map by assigning indices at each point of the object, which correspond to the selected pixon kernel, generating an output object model based on indices within the pixon map.

EFFECT: reduced object noise in a reconstructed image.

21 cl, 14 dwg

 

RELATED APPLICATIONS

The present application claims the priority of provisional patent application U.S. No. 61/476012 filed April 15, 2011, the contents of which are fully incorporated into the present description by reference.

The technical FIELD TO WHICH the INVENTION RELATES.

The invention relates to a method of restoring and improving the signal and, in particular, to a method of adaptive noise reduction in the input object.

BACKGROUND of INVENTION

Optimal extraction of data contained in the signal, requires the elimination of defects such as noise, and instrument limitations. A key area in which the search is conducted optimized extraction and recovery of data is the area of image enhancement. Despite the fact that the devices can be made practically free from noise, remain the signature of the devices associated with the finite spatial, spectral or temporal resolution. At this stage of the recovery image you want to remove the signature devices. The processes of image enhancement and noise sources, and other factors that could adversely affect the data extraction, span a wide range, including astronomical observations and the study of planets, where the springs may be weak and atmospheric noise create noise and distortion, the observation in the m ilitary purposes and to ensure security, where the light may be dim and fast moving targets leads to weak contrast and blur, working with medical images, which are often characterized by lack of clarity, and video, there are limitations associated with the transmission and appliances, and demand response in real time can negatively affect the sharpness and detail of the image.

Digital image processing was developed to provide high-quality reliable restoration of blurred and noisy data, collected by different sensors. This field exists because it is impossible to build devices for working with images, creating images with a constant clear, not distorted by noise in the measurement. However, it is possible mathematically to restore the base image from imperfect data, obtained using real devices, so that information available, but hidden in the data that can be retrieved with less blur and noise. Many such methods use the process in which you create a prediction model and compare it with the data to assess the accuracy of fit of the model to the data.

In this written description, the term "data" refers to any measured value from which to calculate the unknown image using the process is and restore images. The term image refers to as the computed solution and the true underlying image, which serves as the basis for the observed data. The discussion usually clarifies the applied context; in cases of ambiguity, the term "model image" is used to denote the computed solution. It should be noted that the data and the image does not necessarily have to be similar and may even have different dimensions, for example, the purpose of tomographic reconstruction procedures is the determination of the three-dimensional image based on the projected two-dimensional data. The term alternative image is the object, transmitting the idea, namely, that the model can be more General than the image. In the future, these two terms are used as synonyms.

Statisticians have long been sought to limit the parameters used to fit the data to improve the interpretation and prediction accuracy of the approximation. Standard techniques are a subset, which found that some parameters are not significant and excluded from the approximation (e.g., Miller 2002), and ridge regression, in which parameter values limit by adding a regularization term to the evaluation functions used in the approximation (e.g. the, Tikhonov 1963). Tibshirani (1996) combined the two methods in the technique, known as the lasso method, Tibshirani (Least Absolute Shrinkage and Selection (LASSO)).

The need to limit a certain number of parameters in the approximation is compulsory for under defined or poorly defined problems where the number of parameters is greater than or comparable to the number of data points. As noted by the creators of the statistical method of least squares (Gauss 1809) and the method of maximum likelihood (Fisher 1912, 1922), these methods are only valid in the asymptotic limit in which the number of data points exceeds the number of fitted parameters. Beyond the asymptotic limit noise is approximated as a signal, and the approximation loses its interpretative and predictive power.

Puetter and others (2005) reviewed numerous data recovery algorithms used nowadays, including iterative methods for recovering images, which iteratively approximate the model of the image relative to the data. Many iterative schemes of the prior art, is designed to converge to the solution of the maximum likelihood estimator converge slowly, even at their early termination to avoid areapproximately. Faster convergence can be achieved by using matrix Hess the partial derivatives of the second order evaluation function with respect to variable (Hesse 1876). Unfortunately, even when using this approach, the Hessian matrix is too large to calculate when working on large-scale problems often encountered in image restoration, for example, when the image contains a large number of pixels with significant radiation. In such cases, the number of matrix elements can be calculated in the trillions. Matrices of this size simply cannot be treated with modern computers, or even stored in memory.

The desire to limit the number of parameters under defined or poorly defined tasks - sparseness, as it is called now based on a more abstract notion of minimal complexity (Solomonoff 1964; Kolmogorov 1965; Chaitin 1966), which dates back to medieval work of William of Ockham, supporting the economy principle postulates. Simply put, at equal other conditions, a simple explanation better than more complicated explanations.

The solution sparsity, for example, by adding a regularization term norm of l0to the merit function is the N-P complex task, in which the computational costs grow faster than any polynomial in a certain number of parameters. This led to the replacement of the norms of l0the norm of l1(Chen, Donoho & Saunders 1999), so the optimization approximation consider is LNO parameters was solving a convex problem. Candes, Romberg &Tao (2004) took a step forward and demonstrated how to randomly reduce the amount of data required for the approximation provided unrelated, a technique known as "compressed sensing" (compressed recognition). Donoho (2006) demonstrated that when such a condition unrelated among the basis functions used in the parameterization, the solution of minimal norm of l1it is also the most sparse solution.

Disadvantages ways norm l1have two sides. First, many interesting tasks simply do not meet the condition unrelated and are not suitable for methods of norm l1. Secondly, even if they meet the condition unrelated, large-scale problems require excessive computational costs. Thus, although they are convex problems and solved, in principle, they cannot be applied to modern problems with millions or more parameters, this problem also affects traditional statistical methods. Donoho and others (2006) describe how to more effectively apply the random nature of such large-scale tasks, not using the norm of l1.

The pixon method is an effective technique to obtain a minimally complex solutions data based on the pixel - including large-scale problems without having to strictly the sparsity and without conditions unrelated, the required ways, using the norm of l1(see, for example, Pina & Puetter 1993; Puetter & Yahil 1999; Puetter, Gosnell & Yahil 2005, and U.S. patent№5912993, 6353688, 6490374, 6895125, 6993204, 7863574, 7928727, 8014580, 8026846, 8058601, 8058625, 8086011, 8090179, 8094898, 8103487, the contents of which is hereby incorporated into this description by reference). Therefore, the pixon method is applicable for large-scale under defined or poorly defined inverse problems such as image restoration or spectral analysis. Minimal complexity reached by adaptive smoothing in the location of each pixel with the most extensive kernel from the library of kernels, so smoothing with this kernel and all narrower cores provides a reasonable approximation of the fingerprint data of the considered pixel. Map, lookup, what kernel you want to use in each pixel is called the pixon map.

In its modern form recovery pixon consists of three stages. At the first stage it restores pseudoanabaena" without any restrictions pixon. In the second stage this pseudoanabaena used for determining a pixon map. At the third stage, get ready image by incomplete recovery, managed by the pixon map. The second and third steps may be repeated several times, but in practice this is usually not necessary, provided that Thu is the first step was obtained acceptable pseudoanabaena. Cm. Puetter & Yahil (1999), Puetter and others (2005) and U.S. patent№5912993, 6353688, 6490374, 6895125, 6993204, 7863574, 7928727, 8014580, 8058601, 8058625, 8086011, 8090179, 8094898 and 8103487 for more complete descriptions of the pixon method and its application.

In Fig.2 shows the typical system 200 imaging detector 210 images and block 220 recovery pixon. Recovery is based on the pixon method using map P pixon interacting with the algorithm 230 recovery pixon. The pixon method relates to a method, smoothing each point in object space (each, a "point object") by assignment of the form or volume of each point of the object as the basis for pixon smoothing. The object space is the space in which the result of the recovery image and which corresponds to the region of the image which was obtained using the system 200 imaging. (It should be noted that the "image space" is a term synonymous with the term "space object" and the two terms are used interchangeably in the future.) The corresponding data space provided by the data points measured by the detector 210 images.

The pixon method provides high-quality reconstruction of the first image in object space from the measured set d of data in the data space. As prostranstvenno adaptive restore method, the pixon method applies due to data smoothing operation to each point of the object. Thus, the pixon method uses the principle of minimum complexity when assigning to each point of the object function of the pixon kernel, which is the basis of the operation of smoothing. Within a block 220 recovery pixon pixon map P determines which of the pixon kernel functions assigned to each point of the object.

In the system 200 imaging detector 210 detects images and associates measured set of d data block 220 recovery pixon. Block 220 recovery pixon uses a special way adapted algorithms 230 recovery pixon for recovery of the received set of d data object of the first image. Thus, the algorithm 230 recovery pixon uses the matrix H of the system to describe properties of a system 200 imaging and to calculate iteratively improved object image by adjusting the data model, which is the object of the first image. The object of the first image, for example, display device 240 display, using known imaging techniques.

For each point of the object map P pixon provides a pixon kernel function, defined on the basis of the method of minimal complexity. The pixon kernel function is used in the operation of the pixon smoothing used in space is the firmness of the object.

The pixon method can also allow for a concise recognition in the form of ultra-high resolution, using the nonnegativity of images and minimal complexity to restore the image with smaller pixels than the pixels for which the data obtained. It is not a violation of theorem samples by Nyquist (1928) and Shannon (1949) due to the additional conditions of nonnegativity and minimum complexity (for example, Puetter and others, 2005). Spatial frequencies beyond the diffraction limit, truncated data in this way can be restored in the image.

In Fig.3 depicts an exemplary sequence of the process according to the pixon method. The pixon smoothing applied consistently to the standard recovery algorithm.

Using the standard recovery algorithm, the input image to approximate the measured set of d data (step 300). In accordance with the above operator To the pixon kernel, the final calculation of the image is called pseudoanabaena. Map P pixon determine, using pseudoanabaena and measured set of d data (step 310). Pseudoanabaena also is the source object for the operation of the pixon smoothing (step 320). During the operation of the pixon smoothing (step 320) perform smoothing at each point of the object pseudoanabaena via the DRA pixon. (In some versions of existing methods pixon pixon map can also be updated in each iteration by computing the updated image.)

Iterative methods for recovering images iteratively approximate the model image to the measured data and thus minimize the effects of noise on the final image. The result of the recovery algorithm is an approximated image, which is approximated to the measured set of d data according to the rules of the algorithm.

The pixon method approximated the image may be used as an input object for pixon smoothing, to restore the pixon and to determine the pixon map.

The pixon method includes finding the widest possible pixon kernel functions at each point in object space, which together support a sufficient approximation of the object to the measured set of d data. In particular, the pixon map assigns to each point of the object defined pixon kernel function.

The stage at which first calculates pseudoanabaena, which then can be defined pixon map can have disadvantages. This process requires more computation and is associated with the risk of introducing distortions in pseudoanabaena that can distort the pixon map and, consequently, the final restoration of the images. In addition, the definition of the pixon map works worse, if the conversion from object-space to the data space is non-local (Bhatnagar & Cornwell 2004). For example, in interferometry and obtaining images using magnetic resonance imaging data represent the Fourier transform of the image (plus noise), with each wave Fourier (a basic function of the image) is distributed throughout the image. Another example is partially nonlocal transform in tomography. Data represent two-dimensional projections of three-dimensional images (plus noise), the transformation is local in the direction perpendicular to the projection direction, but nonlocal along the direction of projection.

In light of the foregoing, there is a need for an improved method of determining the pixon map within the pixon method.

SUMMARY of the INVENTION

According to the invention described here, the above-mentioned difficulties of the pixon method, consisting of three stages, can be avoided by calculating and updating the pixon map during iteration. Improved approach determines the pixon map from a variable that is used to update the image in the iteration, i.e., "update of the variable, and smoothes this update a variable in an iteration. The updated image is usually also Spa is more at the end of the iteration, using the pixon map defined in an iteration. In contrast, existing methods pixon determine the pixon map of the image after it has been upgraded and transferred to the smoothing of the image, using the pixon map.

According to the present invention updates the variable depends on the way of recovery, but is typically a gradient of the evaluation function or multiplicative coefficient updates (for example, Puetter and others 2005). This updates the variable smooth using pixon kernels and the kernel selected in each coordinate of the image is the most powerful engine for which the ratio between the square of the change updates the variable anti-aliasing and variance of the update variable is less than a predefined threshold value for the engine and all more than the narrow cores. Usually the same core subsequently also used for smoothing the updated image in the coordinate before proceeding to the next iteration. Additional improvement allows the use of "interpolated kernel.

In one aspect of the invention a method to restore the object model from a set of data obtained from a physical process, where the data set contains noise, includes the steps in which: receive a set of data defined in the data space; create a model object is in object space, where the model object contains the set of points of the object; and develop a transformation model of the object from object-space to the data space, the result of which is the data model, where the conversion corresponds to the physical process by which the received data set; choose an evaluation function for determining the approximation of the data model to the data set; determine the update variable object model in object space on the basis of the evaluation functions; perform smoothing renewing variable to determine the smoothed updating the variable in the following way: perform coagulation updating a variable with each of the multiple cores pixon; and choose for each point of the input object, the pixon kernel with the biggest size and the corresponding predefined minimum criteria; generate a pixon map by assigning indices at each point of the input object corresponding to the selected pixon kernel; and generate output containing object model with significantly reduced noise based on the indexes within the pixon map. In one embodiment, the evaluation function is determined using the method of conjugate gradients, and updates the variable represents agradient.

In another aspect of the invention, the permanent machinace aemy media containing pre-recorded software, contains the commands to restore the object model from a set of data obtained from a physical process, where the data set contains noise, and commands include the following: receive a set of data defined in the data space; create a model object in object space, where the object model contains the set of points of the object; and develop a transformation model of the object from object-space to the data space, the result of which is the data model, where the conversion corresponds to the physical process by which the received data set; choose an evaluation function for determining the approximation of the data model to the data set; determine updating a variable object model in object space on the basis of the evaluation functions; perform smoothing renewing variable to determine the smoothed updating the variable in the following way: perform coagulation updating a variable with each of the multiple cores pixon; and choose for each point of the input object, the pixon kernel with the biggest size and the corresponding predefined minimum criteria; generate a pixon map by assigning indices at each point of the input object corresponding to the selected pixon kernel. In what NRN embodiment, the evaluation function determines using the method of conjugate gradients, and updates the variable represents agradient.

A BRIEF DESCRIPTION of GRAPHIC MATERIALS

In Fig.1 depicts a block diagram of a General computing environment in which the present invention can be implemented in practice.

In Fig.2 shows the overall performance of the system imaging prior art, based on the pixon method.

In Fig.3 depicts a flow chart, showing an example of image reconstruction using prior art for the recovery pixon.

In Fig.4 depicts a flow chart, showing an example of image reconstruction using the pixon method according to the present invention.

In Fig.5 depicts a flow chart, showing an example of the alternative recovery process images using the pixon method.

In Fig.6 shows do not contain noise, normal, proton density (PD) SBD "true" image of the brain.

In Fig.7 shows the logarithm (base 10) of the absolute value of the Fourier transform of the image in Fig.6 in the data space.

In Fig.8 shows the image of Fig.6 with a random (white) Gaussian noise added to the image with a standard deviation equal to 3% of the bright waxes image.

In Fig.9 image is Agen logarithm (base 10) of the absolute value of the Fourier transform of the image in Fig.8 in the data space.

In Fig.10 shows the same data as in Fig.9, with truncated high frequency corresponding to the frequency coverage, a limited part of the available frequencies. The data in Fig.10 contain the input information to restore the image shown in Fig.11-14.

In Fig.11 depicts a simple inverse Fourier transform of the data in Fig.10, revealing two types of distortions: correlated (not white) noise and reverberation on sharp edges.

In Fig.12 shows the result of recovery pixon data in Fig.10 factor pixon, 0.3.

In Fig.13 shows the result of recovery pixon data in Fig.10 factor pixon equal to 0.5.

In Fig.14 shows the result of restorations pixon data in Fig.10 factor pixon, equal to 1.0.

DETAILED description of the INVENTION

Before describing aspects of the present invention may be useful to provide a brief description of a suitable computing system environment 100 (Fig.1), which can be implemented in the invention. The computing system environment 100 is only one example of a suitable computing environment and is not intended to introduce any limitations of the scope of use or functionality of the invention. You should also not interpret the computing environment 100 as having any dependency or requirement relating to ubago component or combination of components, depicted in the example operating environment 100.

The invention can work with many other universal or specialized systems computing environments or configurations. Examples of well known computing systems, environments and/or configurations that may be suitable for use with the invention include, but are not limited to: personal computers, server computers, handheld or laptop devices, multiprocessor systems, microprocessor-based, set-top boxes, programmable consumer electronics, network PCs, mini-computers, large mainframe, telephony systems, distributed computing environments that include any of the above systems or devices, and so on

The invention can be described in the General context of instructions executed by a computer, such as program modules, executed by the computer. In General, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement certain abstract data types. Specialists in this field can implement the description and/or figures given here in the form of instructions executed by the computer, which can be embodied in any machine-readable form is ositelu, described below.

The invention can also be implemented in distributed computing environments where tasks are performed by remote processing of data connected by a communication network. In a distributed computing environment, program modules may be located on both local and remote computer storage media including memory devices.

With reference to Fig.1, an exemplary system for implementing the invention includes a General-purpose computing device in the form of a computer 110. Components of computer 110 may include, but not be limited to the following: processor 120, system memory 130, and a system bus 121 that connects various system components including the system memory to the processor 120. The system bus 121 may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus and a local bus using any variant of the architecture of the tire. As an example, but not limitation, such architectures include bus, industry standard architecture (ISA)bus, a microchannel architecture (MCA)bus, enhanced ISA (EISA), local bus Association standards in the field of video electronics (VESA) and the bus connection of peripheral components (PCI), also known is tnou as the expansion bus.

The computer 110 typically includes a variety of machine-readable media. Machine-readable media can be any available media that can be accessed by computer 110 and includes both volatile and nonvolatile media, removable and non-removable media. As an example, but not limitation, computer-readable media may include computer storage devices and communication media. Computer storage devices include volatile and nonvolatile media, removable and non-removable media implemented in any method or technology for storage of information such as machine-readable commands, data structures, program modules or other data. Computer storage devices include, but are not limited to: RAM, ROM, EEPROM, flash memory or other technology storage devices, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and which can accessed by computer 110. Communication media typically include a machine-readable commands with the touch data, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and include any medium for information delivery. The term "modulated data signal" means a signal, in which one or more of its characteristics set or changed in such a manner as to encode information in the signal. As an example, but not limitation, communication media include wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Any combination of the above media should also be included in the scope of the term "machine-readable media".

The system memory 130 includes computer storage device in the form of volatile and/or nonvolatile storage devices, such as permanent memory (ROM) 131 and random access memory (RAM) 132. Basic system 133 input/output (BIOS), containing basic routines that help to transfer information between elements within computer 110, for example, when the computer starts up, is typically stored in ROM 131. RAM 132 typically contains data and/or software modules that are directly available to the processor 120 or processed about what Esarom at the moment. As an example, but not limitation, in Fig.1 illustrates operating system 134, application programs 135, other program modules 136, and program data 137.

The computer 110 may also include other removable/non-removable, volatile/nonvolatile computer storage device. Just as an example, in Fig.1 shows a hard disk drive 141 that reads or writes data on non-removable, nonvolatile magnetic media, the actuator 151 to a magnetic disk drive that reads or writes data on a removable nonvolatile magnetic disk 152, and an actuator 155 optical drive that reads or writes data on a removable nonvolatile optical disk 156 such as a CD-ROM or other optical media. Other removable/non-removable, volatile/non-volatile computer storage device that can be used in the exemplary operating environment include, but are not limited to the following: magnetic cassette tape, flash memory, digital versatile disks, tape with digital video, solid state RAM, solid state ROM, etc., Hard disk drive 141 is typically connected to the system bus 121 via an interface of the non-removable storage devices, such as interface 140, and the actuator 151 for magnetic disks and actuator 155 for optical drives typically connect the s system bus 121 by a removable storage interface device, such as interface 150.

The drives and their associated computer storage device described above and shown in Fig.1, provide storage of computer-readable commands, data structures, program modules and other data for the computer 110. In Fig.1, for example, shows that the hard disk drive 141 stores an operating system 144, application programs 145, other program modules 146, and program data 147. It should be noted that these components may be the same as the operating system 134, application programs 135, other program modules 136, and program data 137, or different from them. In this case, the operating system 144, application programs 145, other program modules 146 and program data 147 assigned to other rooms in order to show that they at least represent different copies.

The user can enter commands and information into the computer 110 through input devices such as a keyboard 162, a microphone 163 (which is an input provided via phone) and pointing device 161, such as a mouse, trackball or touch pad. Other input devices (not illustrated) may include a joystick, game controller, satellite dish, scanner, or so forth These and other input devices are often connected to the processor 20 through an interface 160 user input, connected to the system bus, but may be connected by other interface structures and bus, such as a parallel port, game port or a universal serial bus (USB). A monitor 191 or other type of display device is also connected to system bus 121 via an interface, such as a video interface 190. In addition to the monitor, computers may also include other peripheral output devices such as speakers 197 and printer 196, which may be connected through an output peripheral interface 195.

The computer 110 may operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 180. The remote computer 180 may be a personal computer, handheld device, a server, a router, a network PC, a peer device or other common network node, and typically includes many of the elements or all the elements described above with respect to computer SOFTWARE. Logical connections described in Fig.1 include a local area network (LAN) 171 and a wide area network (WAN) 173, but may also include other networks. Such networking environments are common in offices, corporate computer networks, intranets and the Internet.

When using in a network environment LAN, the computer 110 is connected to the LAN 171 pose the CTV network interface or adapter 170. When used in a WAN network environment, the computer 110 typically includes a modem 172 or other means of connection on the WAN 173, such as the Internet. The modem 172, which may be internal or external, may be connected to the system bus 121 via an interface 160 user input or other suitable mechanism. In a networked environment, program modules depicted relative to the computer 110, or parts thereof, may be stored in a remote storage device. As an example, but not limitation, in Fig.1 illustrates remote application programs 185 permanently stored on a remote computer 180. It should be understood that the depicted network connections are exemplary and may be used other means to establish communication between computers.

In this application, the term "pixon" is used to denote that the term, method, object, etc. refers to the pixon method, i.e. the use of certain forms of points in the smoothing of the image object, as described in U.S. patent No. 5912993, 6895125 and other related patents. For example, assigned to the shape defined by the pixon kernel functions, and the map P pixon stores information about which/which of the pixon kernel functions assigned/assigned to each point of the object.

Approximation to the data is the solution of noisy inverse problems. The data is expressed by the model

where d is an array containing the measured data, I represents an array containing the parameters of the approximation, H is a transformation function from the parameter space into the data space and εis an array containing the noise introduced in the data. For clarity, the notation corresponding to the restoration of the images used in equation (1), i.e. d represents the pixel data and I is the restored image. However, this example is not intended to be limiting, as the invention described herein has wide applicability with respect to any noisy inverse problems that can be solved using the pixon method.

For many applications the transformation H is linear, and the equation (1) can be written in the form

where d and I are considered as vectors and H as a matrix, known as the system matrix. The following description is limited to the linear case of equation (2), but it can be generalized to non-linear problems by linearization, i.e., considering the limited area of the image, in which H(I) is approximately linear.

It should be noted that in d is lnasty d and I can be multidimensional and should not even have the same dimension (for example, in tomography). However, multivariate pixels can always be arranged in the form of long vectors and H can be represented in matrix form. Model data

is a signal part of the data that does not contain noise. She is also the expected value data

since the expected value of the noise, without losing generality, can be identically set to zero for all data points

The covariance matrix of the noise, in General, not equal to zero, and may be a function of position (pixel coordinates) and/or value data model

Typically, the data points are independent, so V is a diagonal matrix, but can also be correlated data, in this case V is off-diagonal non-zero elements.

Image restoration is an inverse problem of solving the equation (2) or, more generally, equation (1) for image I, given data d, the system matrix H and a statistical model of the noise ε. This problem is solved by optimizing the evaluation function of the data given the model data

The choice of the evaluation function depends on the statistics of the noise. Usually, the evaluation function is ybiraut logarithmic likelihood function (LLF), related to the maximum likelihood (e.g., Puetter and others, 2005).

For Gaussian noise LLF reduces to χ2

where the summation over i is carried out in respect of pixel data, where the summation over α is carried out in respect of image pixels, σiis the standard deviation of the Gaussian noise in the pixel i. Gaussian LLF has the advantage that it quadraticity in the image I, so that its gradient is relatively I is linear in I.

For Poisson noise LLF is more complicated nonlinear function

which can be solved by nonlinear optimization (for example, Press and others, 2007) or the use of surrogate functions (Lange, Hunter & Yang 1999). Mighell (1999) proposed to use instead the quadratic approximation to the Poisson LLF, resulting in an undistorted model of the data, even in the limit of small units of account

There are many ways to optimize the evaluation function, but few are suitable for large-scale problems, because the system matrix H and its transposed matrix of HTbecome too large to compute and store - even using the technique of sparse matrices and can be applied only as operators. This leaves essentially two : the BA: the ways of the expectation-maximization (EM) (Richardson 1972; Lucy 1974; Dempster, Laird &Rubin 1977; Shepp &Vardi 1982) or methods of conjugate gradients (CG) (Fox, Huskey & Wilkinson 1948; Hestenes &Stiefel 1952; Press and others, 2007). To minimize standby ordered subsets (OSEM) is accelerated variant of EM, using only a subset of the data in each iteration (Hudson & Larkin 1994). The same procedure can also be applied to CG.

The CG method is carried out by sequential search of the minimum of the descending gradient of the evaluation function. More precisely, he uses directions conjugate gradient representing a linear combination of the gradients (for example, Press and others, 2007). A useful concept is to agradient defined as half of the negative gradient of the evaluation function with respect to the image. For the Gaussian estimator, equation (8), agradient is a

in vector-matrix notation, equation (11) can be written in the form

where

are remnants and the noise variance is a

where Diag(σ2) denotes a diagonal matrix whose diagonal elements are σ2the squares of the standard deviations.

For Poisson noise agradientx γ2evaluation functions Mighell (1999) is a

Agradient Mighell Poisson linear in the image I and can be written in a compact vector-matrix notation, equation (12), where residues are

and the noise variance is a

The CG method can be accelerated considerably by adding pedololitas (e.g., Golub &Van Loan 1996; Saad 2003), changing the gradient of the evaluation function on the

where the linear equation

you can easily solve it. The resulting method is known as predostavlennyy method of conjugate gradients (PCG).

Restrictions can often be solved using the method of projection onto convex sets (Biemond, Lagendijk & Mersereau 1990). For example, the nonnegativity, I≥0, can be forcibly introduced after each iteration by a simple truncation of the negative components of the image to zero and continue as if truncation occurred (Puetter and others 2005). Also useful after each iteration, set to zero any negative component of the conjugate gradient pixels with a zero value of the image in this iteration. This prevents teaching the ment of these pixels to minimize only for to the resulting negative images were truncated to zero at the end of the minimization.

In the invention described here, the pixon map shall update the variable and not from the image after the update and updates the variable smooth in accordance with this card pixon. This eliminates the need for calculating the initial pseudoanabaena because pixon map updating and renewing smooth variable in each iteration.

For the CG method as updating a variable, choose agradient, equation (12). (Predostavlennyy agradient, equation (18), decided the same way.) Agradient smooth with nuclei in the library of the pixon kernels and the kernel selected in each coordinate of the image is the most powerful engine for which the ratio between the square of the change agradient anti-aliasing and dispersion of agradient less than a predefined threshold value for the engine and all more than the narrow cores.

In particular, choose a library of kernel functions that are defined in object space

The zero and first moments of the kernel functions set the following:

and second moments are placed in ascending order

where multi-the crystals approximated, in practice, the summation of the pixels. The second moments are usually designed in such a way as to form an increasing geometric sequence for optimal characterization of multi-scale structures in the image. It should be noted that an important dimension in equations (21)-(23); therefore, the index α of the pixels of the one-dimensional image used previously, replace the vector indices τ and x.

The sequence of changes ΔG(j)the smoothed agradient then obtained by coagulation of agradient alternately with each of the cores and subtracting the initial agradient

In this case, the pixon map is an image indexes, so that each pixel in the selected index is the largest index for which the square of the change in the smoothed agradient less than or equal to the multiplier p2agradient

where p represents a coefficient pixon described below. Smooth agradient obtained by adding to agradient each pixel of the image change of the smoothed agradient corresponding to the index of its pixel

As clearly seen from equation (25), the coefficient pixon p, modifiable by the user, adjusts the power of the pixon smoothing. Most led is the rank of p may allow a larger value of j to satisfy equation (25) in any pixel x, thereby increasing the value of M(x). The result is a stronger smoothing agradient, equation (26). In contrast, the smaller the value of p may limit j lower, thereby reducing M(x) and reducing aliasing. In the result, the user can adjust p to select an optimal balance between noise and aliasing. A large p-value better suppress the noise at the expense of some loss of resolution, while a smaller value of R preserves the resolution at the expense of higher noise levels.

In Fig.4 depicts an exemplary process diagram of the improved method of determining the pixon map in the process of image recovery. At step 400, the image restoration begin by optimizing the evaluation function of the data d, given the data model of equation (7). In an exemplary embodiment, used the method of conjugate gradients (CG). At step 402 CG method is used to determine agradient, which will be used as the update variable (UV). At step 404 perform coagulation agradient every kernel from the library 406 cores pixon smoothing UV. The core selected in each coordinate of the image is the most powerful engine for which the ratio between the square of the change updates the variable anti-aliasing and dispersion update re the military less than a predefined threshold value for the engine and all more than the narrow cores. Form pixon map 410, using the image indexes of the selected engines. Usually the same core subsequently also used for smoothing the updated image 408 in the coordinate before proceeding to the next iteration. According to the present pixon method, iteratively enhanced image is the basis for the output image I, which can be displayed on the display device and/or stored in a storage device.

As noted earlier, the example of the application of image reconstruction is not intended to be limiting, and the improved method is applicable to any process signal restoration using the pixon method. It is possible to generalize the kernel to nonlocal performing more complex aliasing. For example, in the image of the apartment building, containing many identical Windows, it is possible to smooth out all the Windows in the image together using one independent kernel. Alternatively, the data may not be geometric values such as equity prices, in this case, the pixelization replace any indexing scheme for the stock. Integral convolution, equation (24), in such systems replace more General attitude

Usually it is advantageous to keep the normalization condition similar to equation (21)

but the level of the Oia (22)-(23) no longer have meaning and must be replaced by the conditions certain tasks. As for the pixon method, it is important that the kernel functions preserve the order of preference, so that equations (25)-(26) retain their value.

An additional improvement is to create a continuous map pixon with fractional indices" and "intermediate nuclei" by interpolating between trial agravante. This further smoothes agradient and/or allows the use of fewer kernel functions. Interim index pixon is defined as M(x)+δ(x), where M(x) is the integer index pixon defined by equation (25), and δ(x) is the added value that linearly interpolates

and equation (26) is replaced by the equation

appropriate use of interpolated nuclei

Iterative CG method goes as usual (for example, Press and others, 2007), with smoothed agradient replaces the original, unflattened agradient.

It is also useful to smooth continuous pixon map, M(x)+δ(x), with itself, using the interpolated kernel according to equation (31). The rationale for this is that the pixon map should be smoothed in each coordinate of the image in the scale of the width of the pixon kernel corresponding to the index pixon in this coord. is the same. Thus, the smoothing pixon map with itself should not bring in significant additional image smoothing, but it can mitigate the distortions that were introduced in the calculation of the pixon map.

The updated image is usually additionally smooth out after iteration interpolated cores, equation (31). However, additional smoothing may cause some oscillations in the solution by iteration, as the kernel, right smoothing agradient, prone to excessive smoothing of the full image. A simple way to suppress oscillations is the smoothing of the image with the average value of the kernel defined in the current and previous iterations. (For the first iteration of the "previous" kernel is a Delta function.)

In Fig.5 shows an exemplary process diagram of the improved method of determining the pixon map in the recovery process images using interpolated nuclei. At step 500, the image restoration begin by optimizing the evaluation function of the data d, given the data model of equation (7). In an exemplary embodiment, used the method of conjugate gradients (CG). At step 502 CG method is used to determine agradient, which will be used as the update variable (UV). At step 504 perform the coagulation agradient every kernel from the library 506 cores pixon smoothing UV. The core selected in each coordinate of the image is the most powerful engine for which the ratio between the square of the change updates the variable and the variance of the update variable is less than a predefined threshold value for the engine and all more than the narrow cores. Form pixon map 510, using the image indexes of the selected engines. After convolution with kernels from the library of kernels pixon interpolated kernel can be generated at step 508 for additional smoothing variables UV used to create the pixon map. The same interpolated kernel can be used to smooth the updated image 512 in the coordinate before proceeding to the next iteration. According to the present pixon method, iteratively enhanced image is the basis for the output image I, which can be displayed on the display device and/or stored in a storage device.

The variance of agradient important to determine the pixon map, you need to calculate with caution, as the transpose of the system matrix, HTequation (12), creates a correlation among pixels of the image, even if the data are statistically independent. In some cases, for example when HTrepresents the Fourier transform, the variance of agradient can be calculated and Litichevsky. In other ways, a convenient way to Monte Carlo to calculate the variance for large-scale problems is to divide the data into several non-overlapping subsets of the data and the computation of agradient G from equation (12) for each subset, replacing the remainder r is randomly implementation of the noise ε.

where the Superscript s indicates the subset.

Since the expected value of the noise is equal to zero for each pixel, equation (5), the expected value of each gradient subset is also zero

Therefore, in the limit of large number of subsets of variance agradient can be approximated as the sum of the squares of the gradients subset

The relative error in the estimation of the dispersion obtained by the method of Monte Carlo equal to

where S is the number of subsets.

It should be noted that for the Gaussian noise variance agradient depends only on the standard deviation of noise, σ, and not on data or images. Therefore, it does not change with iteration and must be computed only once at the beginning of the recovery image.

The same is not always true for Poisson agradient by Mighellx γ2because the baths [di+1]-1in equation (15) depend on noisy data is a complicated nonlinear way. However, practice has shown that the variance in these terms is less important than the variance of the residuals, equation (16), which can be approximated from the data

Therefore, although the variance of the approximation residuals in equation (36) really depends on the data, it does not depend on the image. Consequently, it also does not change with iteration and can be computed only once at the beginning of the recovery image.

Similar pixon method can also be applied to EAT restorations. However, in this case the problem lies in the fact that the variance of the multiplicative coefficients pack (Richardson 1972; Lucy 1974; Shepp &Vardi 1982) varies with iteration and must be recalculated in each iteration. This greatly increases the computational cost, in addition to the well known slower recovery permit under the EAT method that requires much more iterations to the same extent restore permissions. Together, these factors favor the use of the CG method, and not the EM method.

The following are examples of applications innovative way to restore the ia input signal, using the pixon method. These examples are given only for illustration and are not intended to limit.

Examples

Example 1: Aperture synthesis

Aperture synthesis is a type of interferometry, the mixing signals from a system of telescopes to create images with the same angular resolution as a tool covering the entire system. At each separation and the orientation of the chart petals of the interferometer produces output information representing one component of the Fourier transforms of spatial brightness distribution of the observed object. The image (or "map") source created from these measurements. Aperture synthesis is only possible if the amplitude and the phase of the input signal measured by each telescope. For radio frequencies, it is possible through electronics, while for optical light sources of the electromagnetic field cannot be measured directly and correlated in the software, but must be transferred to the sensitive optics and optical interferonogene.

To create high quality images requires a large number of different separations between the different telescopes (projected separation between any two telescopes, visible from the source of cosmic radiation, referred to as the base) - treba is carried out as many different databases to obtain high-quality images. The number of bases (nb) for a system consisting of n telescopes, calculated by the equation nb=(n2-n)/2. For example, in astronomical radio telescopes very large system (VLA) contains 27 telescopes simultaneously providing 351 independent databases, while most techniques millimeter/submillimeter system (ALMA), currently under construction, when complete will contain 66 telescopes, providing 2145 independent databases. Most interferometers with aperture synthesis using the Earth's rotation to increase the number of orientation of the databases included in the observation. Data collection at different times provides measurements with different divisions and angles telescopes without the need to purchase additional telescopes or manual movement of the telescopes, because the Earth's rotation moves the telescope to the new base. Additional provide flexibility by allowing them to move individual telescopes in different configurations, that provides a powerful variable "approach".

Other uses aperture synthesis include interferometric synthetic aperture radar (IfSAR or InSAR), synthetic aperture radar (SAR) and the radar inverse synthetic aperture (ISAR), the sonar synthetic aperture beamforming and magnetometry with a synthetic aperture.

Initially it was considered necessary to carry out measurements on the merits at each stage and in each orientation of the base up to a certain maximum: similar to the Fourier transform with the full sample formally contains information precisely equivalent to the image of the conventional telescope with the diameter of the aperture is equal to the maximal base, hence the name "aperture synthesis". It was quickly discovered that in many cases useful images can be created with relatively sparse and uneven system databases using methods of nonlinear image reconstruction.

The pixon method is a powerful method for nonlinear image reconstruction, but its use is complicated by the non-local nature of the Fourier transform (Bhatnagar & Cornwell 2004). New method of determining the pixon map according to the present invention can overcome this difficulty.

Example 2: Magnetic resonance imaging

Magnetic resonance imaging (MRI) is a technique of medical imaging used in radiology for detailed visualization of internal structures. MRI uses the property of nuclear magnetic resonance to create the image nuclei of atoms inside the body. The MRI machine uses a powerful magnetic field to align the magnetization of some atomic nuclei in the body, and h is cachestate fields to systematically change the alignment of this magnetization. This causes the kernel to create a rotating magnetic field which can be detected by the scanner and this information recorded to produce an image of the scanned area of the body. The magnetic field gradients cause the kernel at different points to rotate at different speeds. Through the use of gradients in different directions of two-dimensional images or three-dimensional images can be obtained at any arbitrary orientation. MRI is used to create images of each part of the body and is especially useful for tissues with a large number of hydrogen nuclei and a small density contrast, such as the brain, muscles, connective tissue and the majority of tumors.

A large part of the body consists of water molecules. Each molecule of water contains two nuclei or protons of hydrogen. When a person is in a powerful magnetic field of the scanner, the direction of the average magnetic moment many protons align with the field direction. The wireless transmitter include a short period of time, and it creates a changing electromagnetic field. This electromagnetic field has a frequency known as the resonant frequency, for its acquisitions and changes the spin of protons in a magnetic field. After turning off the electromagnetic field the spins of the protons return to thermodynamic the balance and volume re-magnetization is aligned with the static magnetic field. During this return to the initial state is generated RF signal, which can be measured by receiving coils. Protons in different tissues return to their equilibrium state at different speeds return. Different variables tissues, including the spin density, T1 and T2 the time of reset, and streaming and spectral shifts can be used to construct images. By changing scanner settings this effect is used to create contrast between different types of body tissues or between other properties, as in functional MRI (FMRI) and diffusion MRI.

Information about the origin of the signal in three-dimensional space can be obtained by applying additional magnetic fields when scanning. These fields are generated by electric currents flowing through the gradient coil, the changing strength of the magnetic field depending on the position inside the magnet. Because it also leads to the predicted dependence of the frequency of the released signal from its origin, the distribution of the protons in the body can mathematically be recovered from the signal, usually by using the inverse Fourier transform.

One big limitation of MRI is the duration of the scan, which leads to increased patient discomfort the low speed handling of patient information. MRI scanning can be accelerated in one of two ways or a combination of both. The duration of a scan on each radio frequency can be reduced, and/or can reduce the number of scanned frequencies. The first leads to an increase in noise, while the second leads to an incomplete coverage of frequencies, requiring techniques similar aperture synthesis. Nonlinear image restoration pixon can help to reduce noise and to compensate for the lost data Fourier, as shown below.

Unfortunately, there is no "ground truth data" or gold standard for the analysis of MRI data obtained on living organisms. Thus, Database modeling brain (SBD) was established at the University of McGill (the database is publicly available on the world wide web at bic.mni.mcgill.ca/brainweb; Kwan, Evans & Pike 1999). SBD contains a set of realistic MRI data volumes generated by the model MRI. These data can be used by a community of experts neyrovizualizatsiya to evaluate the performance of different methods of evaluation images in conditions with known true information.

Currently SBD contains simulated MRI data of the brain, based on two anatomical models: standard models and models of multiple sclerosis (MS). For both models were simulated full three-dimensional volume data, and which uses three sequences (T1, T2 - weighted proton density (PD)and different values of the thickness of the slices, noise levels and levels of non-uniformity of intensity. This data is available for viewing in three rectangular views (transverse, sagittal and frontal), and is also available for download. For more details about creating SBD is available from public sources.

In Fig.6 shows do not contain noise, normal, proton density (PD) SBD "true" image of the brain, and in Fig.7 shows the logarithm (base 10) of the absolute value converting it into a data space. On both figures, the upper panels show coronal slice (left panel) and sagittal slice (right panel). The bottom panel shows a cross-section. Conversion from object-space to the data space consisted of a two-dimensional Fourier transforms, one transverse slice at a time, and display cyclically shifted in the transverse direction, in order to display the zero frequency at the center of it. In Fig.8 shows the image of Fig.6 with a random (white) Gaussian noise added to the image with a standard deviation equal to 3% of the bright waxes image. In Fig.9 shows the Fourier transform in Fig.8 in the data space. It is seen that the noise dominates over the data at high frequencies (cross-border displayed the th data). In Fig.10 shows the same data as in Fig.9, with truncated high frequency corresponding to the frequency coverage, a limited part of the available frequencies. The data in Fig.10 contain the input information to restore the image.

In Fig.11 depicts a simple inverse Fourier transform of the data, showing two types of distortions. First, the entire image is clearly visible noise; he no longer represents the uncorrelated white noise because the cutoff frequency of the data. Secondly, visible reverb next to the sharp edges caused by the phenomenon, first described by Gibbs (1898, 1899). Non-negative least squares (NNLS), approximated to the data (not shown), is essentially identical to the direct inverse Fourier transform. The differences between these images is visible only on in vitro background that are not of interest, and in any case are very small. A more significant improvement of the image visible in Fig.12-14, which depicts the result of restorations pixon with coefficients pixon, 0.3, and 0.5 and 1.0, respectively. All recovery significantly reduce noise and reverberation on Gibbs, but not by the same amount. As described above in the context of equations (25)-(26), there exists an optimal ratio between noise and aliasing, adjustable by the user through the cylinder is enta pixon p. A large p-value better suppress the noise at the expense of some loss of resolution, while a smaller value of p preserves the resolution at the expense of higher noise levels. This optimal ratio seen in Fig.12-14, which depicts the gain smoothing with increasing p, the resulting small loss of resolution.

Example 3: Computed tomography

Computed tomography (CT) provides a method for diagnosing and measuring for medical and test equipment, with which you can explore the internal structure of the patient or the test object without having in the process of performing surgical procedures on the patient or damage to the tested object. In this case, from different angles are recorded multiple projections of the inspected object, from which it is possible to calculate a three-dimensional description of the object.

The tomographic image is generated by converting the observed projections (data) in the image. For example, in x-ray CT imaging x-rays is directed to the object and the rays are attenuated at different magnitude due to the different structures inside the object. On the other side of the object weakened rays measured by the detectors. Such projections are created by many different angles around the object. These measurements not only contain noise, what about the in addition, the relative level of noise depends on the attenuation. Projection through dense materials such as bone and especially metal, have a lower signal-to-noise ratio than the projection through the muscle tissue, water or other less dense materials. Working with large and spatially variable fluctuations of the number of detected photons often requires statistical smoothing techniques to improve the image.

Approaches statistical image reconstruction problem is to find images that are best suited to measurements according to the (possibly nonlinear) physical models and statistical models. The correct statistical modeling can result in a less noisy image, thereby enabling to reduce the dose of x-ray radiation for the patient.

Example 4: Emission tomography

Emission tomography is a technique of medical radioisotope imaging, creating a three-dimensional image of functional processes in the body, using tomographic techniques, similar to those used in CT. The difference lies in the fact that the gamma-active or positron-emitting radioisotope (called a radionuclide) is injected into the bloodstream of the patient. Gamma-active radionuclides emit a single photon, and the method of imaging is known as the single-photon emission computed tomography (SPECT or sometimes FAT). In contrast to this method, the emitted positrons mutually annihilating with electrons in the body and form two photons moving in opposite directions detected simultaneously; this imaging technique known as positron emission tomography" (PET).

Most of the time marker radioisotope of interest only because of its radioactive properties, attached to a specific ligand for creating radioligand of interest due to their ability to bind to certain types of tissues. This connection allows the combination of the ligand and of the radioisotope (radiopharmaceutical funds) and to associate the received combination with the chosen area of the body, which then (through direct or indirect gamma cure isotope) allows you to visualize the ligand concentration.

Radionuclide scans are increasingly read alongside CT or MRI scans, with this combination provides both anatomic and metabolic information (i.e. information about the structure and biochemical processes). Because radionuclide imaging is most useful in combination with anatomical visualization, modern radionuclide scanners currently have built-in high quality scanners with carried alkemi rows of detectors CT or, recently, MRI. Because the two scans can be performed directly one after the other or even simultaneously, during one session, the patient does not change its position between the two scan types, two sets of images are recorded with greater accuracy, so that the region containing the anomaly on the images obtained by radionuclide imaging can more accurately correlate with the anatomy on CT or MRI images. This is very useful when displaying enlarged images of moving organs or structures with higher anatomical variation, which is more common outside of the brain.

The technique, similar to the restoration of computed tomography (CT)is typically used to create three-dimensional images, although the data set collected during radioisotope imaging, contains far fewer protons than CT, so recovery techniques are more complex. The pixon processing can then be used to improve image quality and/or reducing the dose, administered to the patient.

Example 5: Spectral analysis

The spectrum analyzer measures the amplitude of the input signal versus frequency within the full frequency range of the instrument. The main use is to measure the power spectrum of known and unknown who the shaft signals. The incoming signal is measured by the spectrum analyzer is electric, but the spectral compositions of other signals, such as acoustic pressure waves and optical waves, can be considered by applying an appropriate Converter. By analyzing the spectra of the electrical signals, the dominant frequency, power, distortion, harmonic oscillations, bandwidth and other spectral components of the signal can be considered other spectral components of the signal, which are harder to detect in the waveform time domain. These parameters are useful for the characterization of electronic devices, such as wireless transmitters.

Types of spectrum analyzer due to the methods used to obtain the spectrum of the signal. These types are tunable spectrum analyzers conversion scanner and parsers based on the fast Fourier transform (FFT). Tunable spectrum analyzer with the transformation of the scanner uses a superheterodyne receiver for down-conversion spectrum of the incoming signal using a voltage controlled oscillator, and a frequency Converter) for centering the frequency bandpass filter. Using superheterodyne architecture, a voltage controlled oscillator, perestraivaya frequency range, that allows to consider the entire frequency range of the instrument. Spectrum analyzer FFT computes the fast Fourier transform, thereby converting the incoming signal into its frequency components of the spectrum. Some spectrum analyzers, such as spectrum analyzers in real time, using a hybrid technique, where the incoming signal is first convert down to a lower frequency using superheterodyne technology, and then analyzed using FFT techniques.

This is a one-dimensional example in which range ("image") associated with the input data using the nonlocal Fourier transform. The pixon method can be applied to similar data in the same way as other examples of Fourier transforms.

Sources of information

1. Bhatnagar S, Cornwell TJ. 2004. Astron. Astrophys. 426:747-754.

2. Biemond J, Lagendijk RL, Mersereau RM. 1990. Proc. IEEE 78:856-883.

3. Candes EJ, Romberg J, Tao T. 2004, IEEE Tans. Info. Thry. 52:489-509.

4. Chaitin GJ. 1966. J. Assoc. Comput. Mach. 13:547-569.

5. Chen S, Donoho D, Saunders MA. 1999. SIAM J. Sci. TCS. 20:33-61.

6. Dempster AP, Laird NM, Rubin DB. 1977. J. R. Stat. Soc. 39:1-38.

7. Donoho DL 2006, Com. Pure Appl. Math. 59:797-829.

8. Donoho DL, Tsaig Y, Drori I, Starck JL. 2006. "Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit", Stanford Technical Report.

9. Fisher RA 1912. Messenger Math. 41:155cl60.

10. Fisher RA 1922. Phil. Trans. Roy. Soc. A 222:309-368.

11. FoxL, Huskey HD, Wilkinson JH. 1948. Quart. J. Mech. Appl. Math. 1:149-173.

12. Gauss CF 1809. Theoria Motus Corporum Coeletium in sectionibus conicis solem ambientium, English translation, 1963. Theory of Motion of the Heavenly Bodies (New York: Dover).

13. Gibbs JW. 1898. Nature 59:200.

14. Gibbs JW. 1899. Nature 59:606.

15. Golub GH, Van Loan CF. 1996. Matrix Computations, 3eed. (Baltimore: Johns Hopkins University Press).

16. Hesse LO. 1876. Vorlesungen über Analytische Geometrie des Raumes, Insbesondere über Finishes Zweiter Ordnung, (Leipzig: Teubrier).

17. Hestenes MR, E. Stiefel 1952. J. Res. Nat. Bur. Standards, 49:409-436.

18. Hudson HM, Larkin RS. 1994. IEEE Trans. Med. Imag. 13:601-609.

19. Kolmogorov'AN. 1965. Problems Inf. Transm. 1:4-7.

20. Kwan RKS Evans AC Pike GB 1999. IEEE Trans. Med. Imag. 18:1085-97.

21. Lange K, Hunter DR, Yang I. 2000. J. Comp. Graph. Statist. 9:1-59.

22. Lucy LB. 1974. Astron. J. 79:745-54.

23. Mighell KJ. 1999. Astrophys. J. 518:380-393.

24. Miller, A 2002, Subset Selection in Regression, 2eed. (Boca Raton: Chapman & Hall/CRC).

25. Nyquist H 1928. Trans. AIEE 47:617-644.

26. Piña RK, Puetter RC. 1993. Publ. Astron. Soc. Races.105:630-637.

27. Press WH, Teukolsky SA, Vetterling WT & Flannery BP. 2007. Numerical Recipes, 3eed., (Cambridge: Cambridge University Press).

28. Puetter RC, Gosnell TR & Yahil A 2005. Annu. Rev. Astron. Astrophys. 43:139-194.

29. Puetter RC, Yahil, A. 1999. Astron. Soc. Races. Conf. Ser. 172:307-316.

30. Richardson W. 1972. J. Opt. Soc. Am. 62:55-59.

31. Saad Y. 2003. Iterative Methods for Sparse Linear Systems, 2eed. (Philadelphia: SIAM).

32. Shannon CE. 1949. Proc. Institu. Radio Engineers. 37:10-21.

33. Shepp LA, Vardi y 1982. IEEE Trans. Med. Imaging 1:113-22.

34. Solomonoff RJ. 1964. Inf. Control, 7:1-22.

35. Tibshirani R 1996. J. R. Statist. Soc. 58:267-288.

36. Tikhonov'AN. 1963. Soviet Math. 4:1035-1038.

1. Method to restore the object model from a set of data containing noise, the method includes:
receiving in the processor set of data defined in the data space, and the processor is well coordinated:
the generation of the object model in object space, the object model contains the set of points of the object;
the development of a transformation model of the object from object-space to the data space, the result of which is the data model, this transformation corresponds to the physical process by which the data set;
the choice of the evaluation function to determine the approximation of the data model to the data set;
definition updates variable object model in object space on the basis of the evaluation function;
smoothing renewing variable to determine the smoothed updating variable through:
coagulation updating a variable with each of the multiple cores pixon; and
selection for each point of the input object of the pixon kernel with the biggest size and the corresponding predetermined minimum criterion;
generating a pixon map by assigning indices at each point of the object corresponding to the selected pixon kernel; and
generate output containing object model with significantly reduced noise, on the basis of the indexes within the pixon map.

2. The method according to p. 1, in which the processor provides additional smoothing of the object model by collapsing the model of the object at each point of the object with the selected poison the om pixon according pixon map.

3. The method according to p. 1, characterized in that the evaluation function is determined using the method of conjugate gradients.

4. The method according to p. 3, characterized in that the updating variable represents agradient.

5. The method according to p. 3, wherein the processor additionally provides adding pedololitas.

6. The method according to p. 1, in which the processor further provides:
iterative smoothing renewing variable and updating the pixon map and model of the object based on the smoothed variable before updating until the evaluation function is optimized.

7. The method according to p. 1, in which the processor further provides, after a stage collapse updating the variable, subtract the update variable to determine changes to update the variable.

8. The method according to p. 7, characterized in that the predetermined minimum criterion based on the ratio between the square of the change updates the variable and the variance of the update of the variable.

9. The method according to p. 1, characterized in that the data set contains interferometric data generated in conjunction with the analysis process selected from the group consisting of aperture synthesis interferometric synthetic aperture radar (IfSAR or InSAR), synthetic aperture radar (SAR) and radiology the ora with inverse synthetic aperture (ISAR), sonar synthetic aperture beam forming and magnetometry with a synthetic aperture.

10. The method according to p. 1, characterized in that the data set contains data from magnetic resonance imaging.

11. The method according to p. 1, characterized in that the data set contains the calculated data or data emission tomography.

12. The method according to p. 1, characterized in that the data set contains data of spectral analysis.

13. The method according to p. 1, characterized in that the data set contains the set of incoming signals from various tools and object model with reduced noise contains a single output signal corresponding to a mixture of input signals.

14. Permanent machine-readable media containing prerecorded software, this software includes a command to restore the input signal from a set of data containing noise, when this team include:
obtaining a set of data defined in the data space;
the generation of the object model in object space, the object model contains the set of points of the object;
the development of a transformation model of the object from object-space to the data space, the result of which is the data model, this transformation corresponds to the physical process, e is the PTO which the received data set;
the choice of the evaluation function to determine the approximation of the data model to the data set;
definition updates variable object model in object space on the basis of the evaluation function;
smoothing renewing variable to determine the smoothed updating variable through:
coagulation updating a variable with each of the multiple cores pixon; and
selection for each point of the input object of the pixon kernel with the biggest size and the corresponding predetermined minimum criterion; and
generating a pixon map by assigning indices at each point of the input object corresponding to the selected pixon kernel.

15. Permanent machine-readable medium according to p. 14, further comprising smoothing a data set by coagulation model of the object at each point with the selected pixon kernel according to the pixon map.

16. Permanent machine-readable medium according to p. 14, characterized in that the evaluation function is defined using the method of conjugate gradients.

17. Permanent machine-readable medium according to p. 16, wherein updating the variable represents agradient.

18. Permanent machine-readable medium for p. 17, additionally containing added pedololitas.

19. Permanent machine-readable medium according to p. 14, further including the store:
iterative smoothing renewing variable and updating the pixon map and model of the object based on the iteratively smoothed updating variable up until the evaluation function is optimized.

20. Permanent machine-readable medium according to p. 19, additionally comprising, after step coagulation updates the variable, subtract the update variable to determine changes to update the variable.

21. Permanent machine-readable medium according to p. 20, characterized in that the predetermined minimum criterion based on the ratio between the square of the change updates the variable and the variance of the update variable.



 

Same patents:

FIELD: physics, optics.

SUBSTANCE: invention relates to means of analysing fluorescence traces of an object in a displayed image. The method involves generating a video sequence of frames, dividing said sequence into groups in which the inter-frame difference is less than a given threshold value, calculating the average value of digital codes for frame elements within the groups, determining the maximum value from the obtained average values of digital codes for corresponding frame elements, forming an image of fluorescence traces of the object with the maximum value of digital codes.

EFFECT: low level of fluctuation noise in the resultant image due to maximisation of digital codes of elements of average codes obtained beforehand.

2 dwg

FIELD: radio engineering, communication.

SUBSTANCE: disclosed is a deblocking which includes: a step for detecting direction of an edge, which indicates the direction of change in pixel value of each block, a step for determining direction of a deblocking filter to be applied to a block boundary in accordance with the detected direction of an edge, a target process block containing a block boundary to be deblocked, and a block in contact with the target process block, and a step for applying the deblocking filter to the block boundary in accordance with the determined direction.

EFFECT: providing deblocking, wherein texture is preserved in inclined directions which must be retained in the image, and block noise can be efficiently reduced, and improved efficiency of encoding all video information.

9 cl, 44 dwg

FIELD: information technology.

SUBSTANCE: image composed of macroblocks measuring 16x16 is selected from a reference frame, wherein each macroblock is assigned a pixel band with width "a", which serves as field region, as a motion-compensated image and is considered as the input image for the filtration process. The value "a" is defined according to the number of filter branches with a finite impulse response. The filtration process is performed using a motion-compensated image as the input image and the predicted image measuring 16x16 pixels is transmitted to the output as the output image of the filtration process. The predicted image is added in an adder to the output image of the inverse orthogonal transformation circuit and the summation result is used as a macroblock making up the decoded frame.

EFFECT: generating a predicted image with high accuracy without increasing processor load.

6 cl, 1 dwg

FIELD: information technology.

SUBSTANCE: method involves selecting the high-frequency component of pixel values of an image component; subtracting, from the initial pixel values of the image component, corresponding values of the low-frequency component thereof; calculating mathematical expectation and mean-square deviation of the high-frequency component of all pixels of the image component; dividing the matrix of the high-frequency component into columns or rows and calculating values of mathematical expectation and mean-square deviation of each column or values of mathematical expectation and mean-square deviation of each row; correcting the values of the high-frequency component; an image with reduced noise is formed by summation of values of the low-frequency component and the corrected values of the high-frequency component.

EFFECT: reduced noise in an electronic image.

3 cl, 15 dwg

FIELD: information technology.

SUBSTANCE: deblocking filter 113 adjusts the value of disable_deblocking_filter-idc, slice_alpha_c0_offset_div2 or slice_beta_offset_div2 based on the Activity of an image calculated by an activity calculation unit 141, the total sum of orthogonal transformation coefficients of the image calculated by an orthogonal transformation unit 142, Complexity of the image calculated by the rate control unit 119, or the total sum of prediction errors of the image calculated by a prediction error addition unit 120.

EFFECT: improved image quality through correct deblocking.

8 cl, 7 dwg

FIELD: information technology.

SUBSTANCE: method involves parallel processing of the component of each decomposition level; brightness-contract transformation parameters are determined by forming a function for correcting brightness levels and a function for correcting contrast, forming a matrix of correction factors for third level decomposition contrast using the function for correcting contrast, reconstructing the family of matrices of scaled contrast correction factors for spatial matching on each level of correction factors with values of the detail component.

EFFECT: high quality of displaying digital images.

8 dwg

FIELD: information technologies.

SUBSTANCE: method includes performance of the following operations: digital copy of initial printed document is produced in colour space of RGB, brightness difference is detected, and direction of maximum gradient is determined, current count of image is classified for its affiliation to area of brightness difference or uniform area without sharp changes of brightness, Gauss smoothening of current count is made, if it is classified as belonging to uniform area without sharp changes of brightness, current count is smoothened in anisotropic manner, if it is classified as belonging to the area of brightness difference.

EFFECT: invention makes it possible to carry out fast single-stage descreening of screen-type pattern images with preservation of contour differences and increased accuracy.

5 cl, 9 dwg

FIELD: information technologies.

SUBSTANCE: target image that forms video image is divided into multiple division areas (DA); pass band (PB) width applied to DA is determined; array of filtration ratios (FR) is calculated to realise frequency characteristics corresponding to limitation of band, with application of PB width; image data is filtered with application of FR array; error information value is produced between obtained data and data of initial image, and distribution ratio (DR) is calculated to be used to determine optimal width of PB, on the basis of produced value; optimal width of PB corresponding to DR is defined for each DA, and array of optimal FR is calculated to realise frequency characteristics corresponding to limitation of band, using optimal width of PB; image data of division area is filtered using array of optimal FR; and produced data of each DA are synthesised.

EFFECT: generation of filtered image with specified value of image quality assessment.

29 cl, 27 dwg

FIELD: information technology.

SUBSTANCE: first band pass (BP) is determined based on initial image data; a matrix of filter coefficients (FC) is calculated to obtain frequency characteristics corresponding to limitation of frequency band (FB) using the first BP; data of the first filtered image are generated by filtering data of the initial image using the matrix of first FC; an estimate value of the objective image quality of data of the first filtered image is obtained and the distribution coefficient (DC) is calculated, which is used to determine the optimum BP based on the estimate value of objective image quality; the optimum BP corresponding to the calculated DC is determined using a table in which the corresponding relationship between DC and optimum BP is defined; a matrix of optimum FC is calculated to obtain frequency characteristics corresponding to limitation of FB using the optimum BP; and data of the optimally filtered image is generated by filtering data of the initial image using the matrix of optimum FC.

EFFECT: adaptive image filtering process for providing high-quality image.

3 cl, 11 dwg

FIELD: information technology.

SUBSTANCE: filtration of noise from digital images is based on defining a local structure of the image and on non-local averaging in accordance with the defined structure. The local structure of the image is determined by successively rolling up predefined templates with neighbouring pixels and by selecting a RPC template which gives the least error after rolling up. Noise is filtered from the digital image through weighted averaging of pixel values in the search window.

EFFECT: fast filtration of noise in digital images which provides high quality of noise suppression without causing distortions.

4 cl, 16 dwg

FIELD: digital processing of images, possible use for global and local correction of brightness of digital photographs.

SUBSTANCE: system and method for correcting dark tones in digital photographs contain global contrasting module, module for conversion from RGB color system, module for determining dark tone amplification coefficient, bilateral filtration module, dark tone correction module, module for conversion to RGB color system, random-access memory block, displaying device. Global contrasting module is made with possible correction of global image contrast, module for conversion from RGB color system is made with possible conversion of image from RGB color system to three-component color system, one component of which is image brightness, and two others encode color, module for conversion to RGB color system is made with possible conversion from three-component color system, one of components of which is image brightness, and two others encode color, back to RGB color system, module for determining dark tone amplification coefficient is made with possible computation of global image brightness bar graph and can determine dark tone amplification coefficient based on analysis of signs, calculated from global image brightness bar graph, bilateral filtration module is made with possible execution of bilateral filtration of image brightness channel, dark tone correction module is made with possible correction of dark tones in image brightness channel.

EFFECT: absence of halo-effect.

2 cl, 17 dwg

FIELD: methods for removing noise in an image, possible use for improving quality of image.

SUBSTANCE: in accordance to the invention, effect is achieved due to conversion of brightness of image pixels with noise by means of solving the diffusion equation in non-divergent form, which ensures simultaneous suppression of noise and preservation of image edges.

EFFECT: simplified noise removal and increased quality of resulting digital image.

4 cl, 1 dwg

FIELD: photographic equipment engineering, image processing methods, in particular, methods for automatically correcting red-eye effect.

SUBSTANCE: method includes analysis of additional information about an image; creation of at least one array for storing image point marks; for each image point a color mark is recorded into mark array, if the color of point is a typical color for red eyes and is not a typical color for human skin; filtration of one-component image; for each point of image a boundary mark is recorded into array of marks, and also filter number is recorded into array of marks; on basis of array of marks, connected areas of points are determined; for each connected area of points with consideration of neighborhood, computation of fixed row of features; on basis of features, classification of connected areas of points onto red-eye areas and false areas; connection to red-eye connected area of image points neighboring with points of given area and close in color; connection to connected area of red-eye of image points positioned inside external contour of given area; and change of color of points in connected red-eye area.

EFFECT: ensured high quality of automatic correction of red-eye effect.

10 cl, 8 dwg

FIELD: video technology.

SUBSTANCE: invention refers to video compression, particularly to the image block compression systems. The method of image processing is suggested, which includes the definition of whether the two image blocks are adjacent or not, and whether the two blocks are subdivided or not. If the two blocks are adjacent, then the filtration of block smoothing at one or more border pixels of the two adjacent blocks occurs if it is defined that both of the adjacent blocks are not subdivided.

EFFECT: increase in the block smoothing efficiency with the use of border information.

33 cl, 24 dwg

FIELD: electric engineering.

SUBSTANCE: method includes change of image size in accordance with photocopy size and resolution of printing device, histograms are calculated for absolute values of border images, where border images are produced as a result of high-frequency filtration with convolution kernels of different size, border histogram, logarithm integral is calculated for every histogram, criteria are calculated from array of border histogram logarithm integrals, decision is taken on the basis of criteria about photograph sharpness, user is warned about possibility of printing out of focus picture, if picture as classified as out of focus.

EFFECT: detection of low quality, out of focus digital images, and their automatic exclusion from the process of printing with account of preset size of print and resolution of print.

6 cl, 4 dwg

FIELD: information technologies.

SUBSTANCE: invention refers to video compression technology, specifically to blocking effect correction filter applied in multilayered video coder/decoder. Decision mode of blocking effect correction filtration intensity is offered for frame containing block set, including the stages as follows: making decision on current block and adjacent block corrected for blocking effect; estimating whether current block and adjacent block are coded by means of internal BL mode; and if at least one either current block or adjacent block is coded by means of mode other than internal BL mode, making decision on preset filtration intensity relative to border between current block and adjacent block; and if both current block and adjacent block are coded by means of internal BL mode, making decision on filtration intensity which is lower than that chosen relative to border.

EFFECT: development of decision mode blocking effect correction filtration intensity for frame containing block set which provides proper choice of blocking effect correction filter intensity according to that whether certain block to which blocking effect correction filter is applied, uses internal base layer (BL) mode in video coder/ decoder based on layer set.

13 cl, 20 dwg

FIELD: physics; image processing.

SUBSTANCE: present invention pertains to image processing, and in particular, to the method of complexing digital multispectral half-tone images. Method of complexing digital multispectral half-tone images, including obtaining the initial images, involves breaking down each initial image to low frequency and high frequency components, separate processing of low and high frequency component images, complexing of the components, based on the principle of weighted summation for each pixel, and formation of the resultant image. Each initial image is subjected to multiple-level decomposition by the Haar wavelet through fast discrete static two-dimensional wavelet-transformation with the objective obtaining an approximate component, which is a low frequency image component, and a family of detail components, which are high frequency image components. The values of the matrix of energy characteristics of pixels are determined at all decomposition levels for each image. All detail components are filtered and the detail components are corrected through adaptive change of the values of the detail components in accordance with the inter-level dynamics of their energy characteristics. The noise microstructure is removed through adaptive threshold cut of the values of detail components on each decomposition level. The correcting brightness function and the correcting contrast function are calculated for each decomposition level, the parameter of which is a value of the approximate component. Brightness of ranges of each decomposition level is smoothed out through transformation of the approximate components by correcting brightness functions. The detail components of the contrast correcting function are transformed. A weight function is calculated for each decomposition level, the parameter of which is a value of the energy characteristic. The component of each synthesised image for each pixel at each decomposition level is calculated by weighted summation of the corresponding components of decomposing initial images using weight functions. All detail components of the synthesised image are filtered, and the detail components are corrected through adaptive change of the values of detail components in accordance with the inter-level dynamics of their energy characteristics. Noise microstructures are eliminated through adaptive threshold cut of the values of detail components at each decomposition level. The brightness correcting function and the contrast correcting function are calculated, the parameter of which is the value of approximate components of the synthesised image. The approximate component of the correcting brightness function is transformed. The detail components of the contrast correcting function are transformed. The synthesised image is formed through reconstruction using reverse fast discrete static two-dimensional wavelet-transformation, applied to the detail components of the synthesised image and approximate component of the synthesised image. The brightness range of the resulting image is matched with parameters of the video system.

EFFECT: obtaining a high quality image, containing informative image elements of the same scene, obtained in different spectral ranges.

9 dwg

FIELD: physics; processing of images.

SUBSTANCE: invention is related to the field of digital X-ray images processing. Input image is exposed to gamma-correction: extraction of square root for approximation of Poisson noise by model of additive noise distributed according to normal law; for multiplicative model of noise logarithmic conversion is performed; single-level wavelet transform of input image is done, on the basis of which wavelet coefficients are partitioned block-by-block, and standard deviation of noise for every block is assessed; prepared block ratings of noise are smoothened and interpolated by size of initial image, which gives continuously changing and locally adapting assessment of noise for the whole image; initial image is exposed to packet stationary wavelet transform by preset number of decay levels; on the basis of noise level assessment calculated at stage 2, coefficients of transform are exposed to processing with adaptive non-linear operator, which performs threshold suppression of noise and separation of image parts; reverse stationary wavelet transform is done, at that produced image with reduced level of noise and highlighted parts is exposed to reverse gamma-transform.

EFFECT: simultaneous suppression of noise and higher contrast of X-ray images.

5 dwg

FIELD: physics, processing of images.

SUBSTANCE: invention concerns numeral photo, and in particular, the analysis of quality of the numeral image. Method of revealing of unitised contortions is offered at JPEG-coding, at which: estimate the size of the coding block concerning the demanded resolution of a press; spot for each boundary of the block the approximate metric of discernability of contortion at the coding block transformation in case, the size of the coding block is a distinguishable human eye; Classify, in a case when discernability of contortions at coding transformation exceeds the predetermined threshold, boundary of the block or as boundary which demands correction for elimination of unitised contortions or as boundary which is not subject to unitised contortions, by application of the binary qualifier to the vector of the characteristic signs calculated by means of use proquantised DCT of coefficients of the adjacent blocks and a matrix of quantisation of the image.

EFFECT: increase of reliability of detection of unitised contortions at use of the underload computing and temporary resources.

4 cl, 4 dwg

FIELD: physics, computation technology.

SUBSTANCE: invention concerns technology of video compression, particularly deblocking filters. Invention claims deblocking filter applied in videocoder/videodecoder based on multiple layers. Process of deblocking filter power (filtration power) selection during deblocking filtration in respect of margin between current block encoded in intra-BL mode and adjoining block involves determination of whether current or adjoining block has coefficients. Filter power is selected as first filter power if current or adjoining block features coefficients; and filter power is selected as second filter power if current or adjoining block does not have coefficients, So that first filter power exceeds second filter power.

EFFECT: enhanced efficiency of video deblocking.

22 cl, 13 dwg

Up!