# Adaptive two-dimensional method of multiplying estimates and apparatus for realising said method

FIELD: information technology.

SUBSTANCE: apparatus has an input realisation storage unit, a unit for determining quasi-stationarity areas, a mask forming unit, an element-by-element multiplier, an approximation unit, an estimate storage unit, an estimate averaging unit, a useful component estimate storage unit, a current row counter, delay units, an averaging signal generator, a current column counter and a clock pulse generator.

EFFECT: two dimensional estimation of the useful component in conditions with insufficient prior information on statistical characteristics of additive noise and the useful component function.

2 cl, 3 dwg

The present invention relates to information-measuring device and can be used in computing, control systems and image processing.

In General, a simplified mathematical model of two-dimensional signal (image) is a two-dimensional discrete sequence of Y_{i,j},,type:

where S_{i,j}- low frequency, slowly varying useful component;

η_{i,j}additive noise component, distributed according to a Gaussian law with zero mean and constant variance;

N is the number of rows, M is the number of columns of the two-dimensional array image.

The main task - allocation of two-dimensional assessment of the useful component in the conditions of insufficient a priori information about the statistical characteristics of the additive noise and the useful component.

A similar problem can occur: 1) in the work receiving / transmitting devices or far space communications; 2) in radio engineering in signal processing; 3) digital image processing.

There is a method of moving average [R. Gonzalez Digital image processing/ Gonsales, Rwoods. - M.: The Technosphere. - 2005. - S. 1072]. To use the residual one realization of Y_{
i,j},,the original process.

For the original image is determined by the size of the mask smoothing filter m, i.e. a natural number of m<N. the moving average Method involves the memorization of the original image Y_{i,j},define the size of the filter mask m (the width of the "sliding window"), for which the computation of the arithmetic mean,, replacement of the Central values of Y_{i,j},found averageshift "sliding window" on one value to the right, calculate the arithmetic average of the selected values of realization, and so as long as the filter mask will not move around the image.

The width of the "window" choose odd, because the smoothed value is calculated for the Central value.

Signs of a device similar to the matching characteristics of the proposed technical solution, the following: memorizing discrete signal, the allocation of time segments, finding the arithmetic mean value of the signal is caught in the selected periods of time, replacing the original two-dimensional discrete implementation of the measurement results of the smoothed values.

Disadvantages and is known devices are:

- inability to process rows or columns of the image at the boundaries of the mask if the center of the filter is approaching the borders of the image;

- the moving average method calls residuals autocorrelation, even if she was not in the original useful component (the effect of the Slutsk-Yul).

Barriers to achieving the desired technical result are as follows:

- if the width of the "window" smoothing equal to 2P+1, the first p and last p values of the initial implementation of the measurement results is not treated;

because of the Central importance of the "window" smoothing is calculated as the arithmetic average of the neighbouring values assessment is a useful component become dependent.

As a non-linear filters are filters based on rank statistics [R. Gonzalez Digital image processing/ Gonsales, Rwoods. - M.: The Technosphere. - 2005. - S. 1072]. The response of such a filter is determined by pre-ordering (ranking) values of the pixels covered by the mask filter, and then select the value on a specific position in an ordered sequence (i.e. having a certain rank). Filtering is reduced to the replacement of the original values (in the center of the mask) on the output value of the response of the filter. On the more well-known median filter, which replaces the Central value of the filter mask on the median value of the distribution of all values of the measurements that belong to the scope of the filter mask. In order to perform median filtering for image element, you must first be sorted by ascending values of the pixels inside the mask, then find the median value and assign the value of the processed item.

Signs of a device similar to the matching characteristics of the proposed technical solution, the following: memorizing two-dimensional input signal, the allocation of time segments, replacing the input and results of measurement of the smoothed values.

The disadvantages of the known devices are:

- inability to process rows or columns of the image at the boundaries of the mask if the center of the filter is approaching the borders of the image;

- due to the nonlinearity of the way to handle it is impossible to clearly distinguish between the effect of median filtering on the signal and the noise;

- median smoothing can only be considered as an effective method of pre-processing the input and results of measurements in the case of impulse noise.

Barriers to achieving the desired technical result are as follows:

- median filtering is nainan the m processing method;

- the dependence of the efficiency of the smoothing of the measurement results on the shape of the useful and noise component.

The structural scheme of the device that implements the method, comprises a generator of clock pulses, a switch, a control unit, a register storing unit rank, the block selecting the middle value, the output register that stores initial discrete implementation of the measurement results.

The known method of least squares and device for piecewise linear approximation [Bendat J., Persol A. Applied analysis of random data: TRANS. from English. - M.: Mir, 1989. - 540 S., copyright certificate №1624479]. To use this method rather one-dimensional realization of Y_{1}, Y_{2},..., Y_{N}the original process.

The method of least squares allows for measurement result Y_{1}, Y_{2},..., Y_{N}the original process to obtain an estimate,minimizing the target function of the form:

.

In the case whenis a polynomial of the first degreethe coefficients a and b can be found by minimizing the target function of the form:

.

Differentiating the expression for a and b and equating to zero, we obtain a system of linear equations:

.

The solution of the system is:

,

.

When evaluatingthe sum of the squared deviations of values from the values of the realization of the measurements is minimal.

Signs of a device similar to the matching characteristics of the proposed technical solution, the following: memorizing discrete signal, the approximation by the method of least squares, replacing the original discrete implementation of the results of measurements approximated values.

The disadvantages of this method are:

- when using this method requires a priori information about the function of the useful signal;

- useful error component is along the implementation, in the General case, nonlinear dependence and reaches its maximum values at the boundaries of the interval of approximation;

- when polinomialnoi valuation models useful component of a rigorous solution to the problem of minimizing the objective function of the method of least squares is not always there because of the nonlinearity of the solved system of equations;

- limitation of the method of least squares to the parallelization and the construction of a multi-channel processing.

Barriers to achieving the desired technical result are as follows;

- efficiency the evaluation of the useful component depends on the volume of sales, the statistical characteristics of the additive noise and the availability of a priori information on the functional dependency models are useful component.

The structural scheme of the device for piecewise linear approximation contains a group of series-connected registers, the first and second myCitadel, the adder, the first and second accumulating adders, and delay elements, a generator of clock pulses, two multipliers and two divider by a constant factor.

Closest to the invention is a method of selection trend by multiplication estimates his only source implementation (RAZOR) and device for its implementation (patent No. 2207622, IPC 7 G06F 17/18).

The considered device-prototype assumes: 1) memorizing input sales_{1},_{2},..., y_{n}2) split the input on potentially random numbers having a uniform distribution law; 3) test conditions that potentially include not less than L values of the initial implementation, if the condition is not met, then the newly generated random number partitioning; 4) the presence on each pointervalue input realization estimates of the coefficients of the approximating polynomial*and*+bt+ct^{2}using the method of least squares; 5) repeat the procedures in paragraphs 2-4 To time; (6) finding a smoothing function as Wed is the last arithmetic "piecewise quadratic" approximating functions in each moment of time.

Device for selection trend by the method of reproduction estimates his only source implementation (RAZOR) contains a block of storage of the measurement results, switches, random number generator, the block address associated values, the power ranking, register storing a sample of random numbers, blocks of approximation, the storage registers of the estimated arithmetic summing device, the storage unit estimates the useful component, the processor clock.

The disadvantages of the known devices of the prototype are:

- the impossibility of implementing the known method of RAZI in real-time and large computational costs;

- lack of practical guidelines for choosing the number of intervals partitioning and the number of outbreaks of estimates.

Barriers to achieving the desired technical result are as follows:

- to use the method of reproduction is necessary to remember all the input implementation.

The essence of the proposed adaptive two-dimensional method of propagation estimates is as follows.

A simplified mathematical model of two-dimensional input signal is submitted in accordance with the expression (1).

For the formation of adaptive areas of two-dimensional signal for each pixel value are eight directions
(figure 1), which specify the intervals of quasi-stationarity. The condition of quasi-stationarity is tested by calculating the random variable τ is equal to the sum of the number of inversions of the values of the pixels in each of eight directions (figure 1) two-dimensional signal Y_{i,j},,.

For example, the sum of the number of inversions for direction 5 is equal to:

,

,

where i=const, j=const; Y_{i,j}- the current value of the image pixel with coordinates (i,j); Y_{i+l,j}l=i+1...d - subsequent values of pixels in the j-th column (in the direction of 5), d≤R, R is the maximum length of the interval of quasi-stationarity.

The number of combinations, for which we compute the sum of the inverses is:

.

The first alternative (decreasing signal) is accepted if:

The rule for the adoption of the second alternative (increased signal) is:

.

The hypothesis of stationarity of the signal, if a_{2}≤τ_{d}≤c_{1}where α is a priori-defined error value of the first kind.

Received the boundaries of the intervals for each of the eight sectors formed by lines 1-2, 2-3, 3-4, 5-6, 7-8, 8-1, formed the field of quasi-stationarity. D is I used linear interpolation boundaries adjacent intervals the equation of a straight line, passing through two points:

,,

where (i_{1}I ,j_{1}) - coordinates of the boundary direction h, (i_{2}I ,j_{2}) - coordinates of the border areas h+1.

For directionson the image for a one-dimensional implementations, derived from the values of pixels on the vertical and diagonal directions from the Central pixel of the input image, determines the intervals of quasi-stationarity using the method of inversion. These boundaries allow you to get the intervals with a monotonic change the brightness of the signal. Further, all eight of the received sectors are combined into one region Ω. Thus, for each pixel is formed at the pixels with similar brightness value.

Pixel values that fall between all the directions and the interpolating straight lines passing through the boundaries of the intervals of quasi-stationarity, are combined into one region Ω and is approximated by a surface of the first order of the formwhere ω_{i,j},the values of the binary mask, which takes a value equal to:

,,.

The values of the coefficients a, b and C are determined using a two-dimensional way of Naiman is their squares [Patent No. 2362207 Russian Federation, C2, IPC G06F 17/17. 2007127727/09; statements. 19.07.2007; publ. 20.07.2009, bull. No. 20], for finding which minimizes the target function of the form:

Differentiating expression (2) for a, b and C and equating to zero, we obtain a system of linear equations:

The solution of system (3) is:

The procedure for obtaining the domain Ω and the calculation of estimatesis repeated for each pixel value Y_{i,j},when a weight function W_{i,j},value which is equal to the number multiplied estimates for each pixel.

The resulting estimate of the imageis defined as the arithmetic mean multiplied adaptive assessments:

,.

The algorithm (figure 2) consists of the following steps:

- records the values of the input two-dimensional signal Y_{i,j},,;

- parameters method: value error probability of the rst kind α and the maximum length of the interval of quasi-stationarity R;

- calculated random variable

- tests the hypothesis of stationarity of the signal with the_{2}≤τ_{d}≤C_{1}, which is the formation of a binary mask ω_{i,j},;

- calculated scoreusing the approximation of values of Y_{i,j}surface of the first order of the formwhereand calculates a weight function W_{i,j},,;

this procedure is repeated for all values of the pixels of the original image Y_{i,j},,, resulting in a set of estimates;

- determined the resulting assessmentas the weighted sum of multiplied adaptive estimationwhere,.

A device for processing images based on adaptive two-dimensional method of propagation estimates (figure 3) contains the block storage input 1, input by the information input device, the output of which is connected to the first input element of the multiplier 4 is the first input unit to identify areas of quasi-stationarity 2, the output of which is connected to the input of the block forming the mask 3, the output of which is connected to the second input element of the multiplier 4, the output of which is connected to the input of the block approximation 5, the output of which is connected to the first input of the storage unit assessments 6, the output of which is connected to the first input of the block averaging estimates 7, the output of which is connected to the input of the storage unit estimates the useful component 8, whose output is an information output device; the output of the counter current line 9.1 connected to the second input of the block defining areas of quasi-stationarity 2 and the input of the delay block, 9.2, the output of which is connected to the fourth input element of the multiplier 4 and the input of the delay block, 9.3, the output of which is connected to the second input of the storage unit assessments 6 and the first input oscillator signal averaging 9.7, the output of which is connected to the second input of block averaging estimates 7; the output of the counter current column 9.4 connected to the third input of the unit to identify areas of quasi-stationarity 2 and the input of the delay unit 9.5, the output of which is connected to the third input element of the multiplier 4 and the input of the delay block, 9.6, the output of which is connected to the third input of the storage unit assessments 6 and the second input oscillator signal averaging 9.7; simultaneous operation of the device is provided by the clock 10.

The device for about what abode images based on adaptive two-dimensional method of propagation estimates is as follows. Each time you select one of the points of the original image. For it is the region with pixels of similar brightness, using the method of inversion. For each of the received field is the value approximation of two-dimensional signal plane, opisyvayuschaya equation of first degree with two-dimensional method of least squares. Thus, it turns out lots of overlapping estimates obtained regions. The resulting two-dimensional assessment of the useful component is defined as the average volume of the estimates. The obtained values are received at the output device.

Device for image processing based on the two-dimensional method of propagation estimates is as follows. In the storage unit of input 1 is written to the original two-dimensional signal. Blocks counter current line 9.1 and counter current column 9.4 form the coordinates of the pixel to be processed in a given time. The coordinates are sent to the input unit to identify areas of quasi-stationarity 2. Selects pixel values that are close to the selected, from the storage unit of the input 1 and the coordinates of pixels that belong to the scope of similar brightness. The obtained coordinates are passed to the block formation of the mask 3, where the mask is formed of a fixed size, the soda is containing "0" in the pixel coordinates, not owned by the received field, and "1" for belonging. The center of the mask corresponding to the currently selected pixel whose coordinates are the coordinates of the mask. The resulting mask is served on fractional multiplier 4, where by elementwise multiplication of the pixels of the original image on the mask, given its coordinates allocated area coming next on the block approximation 5. The score achieved by fitting a surface of the first order method of least squares, is stored in the storage unit assessments 6, in which in addition to the evaluation remembered and its coordinates received from the meters of line numbers 9.1 and column 9.4 through the delay unit. Sequentially iterates over all pixels of the image, the estimates are stored in the storage unit assessments 6. At the end of the search block generate signal averaging 9.7 delivers on the block averaging estimates 7 signal, and then stored in the unit 6 estimates are averaged, and the storage unit estimates the useful component 8 is remembered estimated useful component. Synchronous operation of the device is provided by the clock 10.

The technical result - the allocation of two-dimensional assessment of the useful component in the conditions of insufficient a priori information about the statistical characteristics of the additive noise and the funk is AI useful component.

1. Adaptive two-dimensional reproduction method estimates based on the approximation of the discrete values of the initial implementation by minimizing the objective function on the basis of the method of least squares and obtain the resulting estimate by averaging multiplied assessments, characterized in that the spacing of the split areas of the approximation is determined luminance adaptive to changes in the signal using the method of inversion, which is the formation for each pixel in the image local quasi-stationary region in the form of a binary mask for each pixel in the image is analyzed eight adjacent areas on the condition of stationarity of the signal by calculating the sum of the number of inversions of the pixel values of the two threshold values; if the sum of the number of inversions belongs to the interval thresholds, the decision on the stationarity of the signal, otherwise the decision on the nonstationarity of the signal; on the coordinates of the eight pixels, for which the decision is made to nonstationarity, is formed of a binary mask; calculated score in each local area by using the approximation of the discrete values of the initial implementation of the surface of the first order and multiplication by a binary mask; this procedure is repeated for all values of the pixels of the source shows the I, the result set of estimates.

2. The device for implementing adaptive two-dimensional method of propagation estimates that contains the block storage input implementation, the entrance of which is an information input device, the block approximation, the storage unit estimates the useful component, the generator of clock pulses, characterized in that the output of the storage unit of the input implement is connected to the first input element of the multiplier and the first input unit to identify areas of quasi-stationarity, the output of which is connected to the input of the block forming the mask, the output of which is connected to the second input element of the multiplier, the output of which is connected to the input of the block approximation, the output of which is connected to the first input of the storage unit assessments, the output of which is connected to the first input block averaging of the estimates, the output of which is connected to the input of the storage unit estimates the useful component, whose output is an information output device; the output of the counter current line connected to the second input of the block defining areas of quasi-stationarity and the input of the delay block, 9.2, the output of which is connected to the fourth input element of the multiplier and the input of the delay block, 9.3, the output of which is connected to the second input of the storage unit assessments and the first input oscillator signal averaging, the output of which the CSO is connected to the second input of the block averaging estimates; the output of the counter current column is connected to the third input of the unit to identify areas of quasi-stationarity and the input of the delay unit 9.5, the output of which is connected to the third input element of the multiplier and the input of the delay block, 9.6, the output of which is connected to the third input of the storage unit estimates and the second input oscillator signal averaging; the synchronisation device is provided with clock pulses.

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