RU2288547C1 - Message compression and recovery method - Google Patents

Abstract

FIELD: electrical communications; data digital computation and processing including reduction of transferred information redundancy.

SUBSTANCE: proposed message compression and recovery method includes pre-generation of random quadrature matrix measuring m x m constituents and k random key matrices measuring N x m and m x N constituents on transmitting and receiving ends, and generation of quantum reading matrix of fixed half-tone video pattern measuring M x M constituents. Matrices obtained are transformed to digital form basing on addition and averaging of A images, each image being presented in the form of product of three matrices, that is, two random rectangular matrices measuring N x m and m x N constituents and one random quadrature matrix measuring m x m constituents. Transferred to communication channel are constituents of rectangular matrix measuring N x m constituents. Matrix of recovered quantum readings of fixed half-tone video pattern measuring M x M constituents is generated basing on rectangular matrix measuring N x m constituents received from communication channel as well as on random quadrature matrix measuring m x m constituents and random rectangular matrix of m x N constituents, and is used to shape fixed half-tone video pattern.

EFFECT: enhanced error resistance in digital communication channel during message compression and recovery.

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Description

The invention relates to the field of telecommunications, and in particular to methods of digital computing and data processing with reduced redundancy of transmitted information. The proposed method can be used to transmit stationary video images on digital communication channels with errors. The invention relates to a class of transform-based encoding-recovery methods.

Known methods for encoding video images based on pulse-code modulation, differential pulse-code modulation, statistical coding and prediction coding, see, for example, the book: W. Prett. Digital image processing. Part 2. - M .: Mir, 1982, p.641-688. These methods involve the encoding of images with bitwise processing, when a continuous video signal is converted into a sequence of quantized samples and then represented by code words in the form of zeros and ones.

Conversion-based encoding methods are also known, see, for example, the book: N. Ahmed, K. R. Rao. Orthogonal transformations when processing digital signals. - M .: Radio and communication, 1980, p. 192-201, including the performance of three operations: first, the image undergoes two-dimensional orthogonal transformation, the resulting conversion coefficients are quantized and encoded for transmission over the communication channel.

The disadvantage of the above methods - analogues is the relatively low speed of message transmission for a given quality of their recovery, as well as low resistance to errors in the digital communication channel.

There is a method of compression and restoration of voice messages described in RF patent No. 22463, IPC ⁷ G 10 L 19/00, 2005, which provides the correction of errors that occur in transmitted digital sequences under the influence of instability of the communication channel parameters and allows information transfer on low-speed digital communication channels. The disadvantage of this method is the relatively low quality of information recovery when the probability of error in the communication channel 10 ^-4 .

The closest in technical essence to the claimed method is the method of compression and restoration of voice messages described in the patent of the Russian Federation No. 2244963, IPC ⁷ H 04 N 7/30, from 2005

The known prototype method, which consists in the fact that previously on the transmitting and receiving sides, a random square matrix of size m × m elements is identical generated. Present information digital signal in the form of a matrix of normalized values. Random rectangular matrices of size N × m and m × N elements are generated, converted by dividing the elements of each row of a random rectangular matrix of size Nxm elements by the sum of units of the corresponding row and dividing the elements of each column by a random rectangular matrix of size m × N elements by the sum of units of the corresponding column . Then, the resulting matrix of N × N elements is calculated by successively multiplying the transformed random rectangular matrix of size Nxm by a random square matrix of size m × m and by the transformed random rectangular matrix of size m × N elements. Next, the standard error is calculated between the elements of the resulting matrix of size NxN elements and the elements of the matrix of normalized values of size N × N elements. After that each element of random rectangular matrices of size N × m and m × N elements is sequentially inverted, and after the inversion of each element in a random rectangular matrix, it is transformed by dividing the elements of each row of a random rectangular matrix with an inverted element of size N · m elements by the sum of units of the corresponding rows and dividing the elements of each column of a random rectangular matrix with an inverted element of size m × N elements by the sum of the units of the corresponding column. Recalculate the resulting matrix of N × N elements by successively multiplying the transformed random rectangular matrix with an inverted element of size N × m by a random square matrix of size m × m and the transformed random rectangular matrix with an inverted element of size m × N. Then calculate the standard error between the elements of the recalculated resulting matrix of size N × N elements with elements of the matrix of normalized values of size N × N elements. A random rectangular matrix of size N × N is transmitted over the communication channel. This matrix is received from the communication channel and the received random rectangular N × m and m × N matrices are converted at the receiving end by dividing the row elements of each random rectangular matrix of N × m elements by the sum of the units of the corresponding row and dividing the elements of each column of a random rectangular matrix of size m × N elements for the sum of units of the corresponding column. The resulting matrix of N × N elements is calculated by successively multiplying the transformed random rectangular matrix of size N × m by a random square matrix of size m × m and by the transformed random rectangular matrix of size m × N. Form a digital information signal. At the receiving and transmitting sides, k random key matrices of size N × m and m × N elements are additionally generated. Each element of a random square matrix of size mxm elements belongs to the range of -500 ÷ +500; k matrices of quantized samples of a stationary grayscale image with dimensions M × M, where k> 1, are taken as a digital information signal.

где i=1, 2, ..., N, j=1, 2, ..., N. В качестве случайной прямоугольной матрицы размером mxN элементов принимают на передающей стороне транспонированную случайную прямоугольную матрицу размером N×m элементов. Формируют k матриц коэффициентов двумерного дискретно-косинусного преобразования размером М×М элементов путем последовательного перемножения матрицы дискретно-косинусного преобразования размером М×М элементов на каждую матрицу квантованных отсчетов неподвижного полутонового видеоизображения размером М×М элементов и на транспонированную матрицу дискретно-косинусного преобразования размером М×М элементов. Далее формируют k матриц коэффициентов двумерного дискретно-косинусного преобразования размером N×N элементов, по формуле A_g(i,j)=L_g(i,j), где i=1, 2, ..., N, j=1, 2, ..., N, g=1, 2, ..., k, Lg(i,j)-i,j-й элемент g-й матрицы коэффициентов двумерного дискретного косинусного преобразования размером М×М элементов, Ag(i,j)-i,j-й элемент g-й матрицы коэффициентов двумерного дискретно-косинусного преобразования размером N×N элементов, причем выбирают N<M. Затем формируют k матриц нормированных значений размером N×N элементов путем умножения каждого коэффициента матрицы коэффициентов двумерного дискретно-косинусного преобразования размером N×N элементов A_g(I,j) на соответствующий ему элемент нормировочной матрицы размером N×N элементов. Каждую из ключевых матриц размерами N×m и m×N элементов суммируют по модулю 2 соответственно с прямой и транспонированной случайной прямоугольной матрицей размерами N×m и m×N элементов, а после вычисления среднеквадратической ошибки между соответствующими элементами каждой результирующей матрицы размером N×N элементов и матрицы нормированных значений размером N×N элементов, вычисляют их итоговую сумму. После инвертирования каждого элемента случайной прямоугольной матрицы размером N×m полученную итоговую сумму сравнивают с предыдущей итоговой суммой. По каналу связи передают случайную прямоугольную матрицу размером N×m элементов, а на приемной стороне после перемножения k случайных матриц размерами N×m на случайную матрицу размером m×m и на k случайных матриц размерами m×N преобразуют результирующие матрицы размерами N×N элементов путем поэлементного деления их элементов на соответствующие элементы нормировочной матрицы размером N×N элементов. Полученные k матрицы восстановленных коэффициентов размерами N×N элементов дополняют нулями до размеров М×М элементов. Восстанавливают k матриц неподвижных полутоновых изображений путем последовательного перемножения транспонированной матрицы дискретно-косинусного преобразования размером М×М элементов на k матриц восстановленных коэффициентов двумерного дискретно-косинусного преобразования размером М×М элементов и на матрицу дискретно-косинусного преобразования размером М×М элементов. Для формирования k матриц квантованных отсчетов неподвижного полутонового видеоизображения размерами М×М элементов каждому ее элементу S_g(x,y), где х=1, 2, ..., М, у=1, 2, ..., М, g=1, 2, ..., k, присваивают квантованное значение соответствующего пиксела g неподвижных полутоновых видеоизображений, размером N×N. Для представления k матриц квантованных отсчетов неподвижного полутонового видеоизображения размером М×М элементов в виде k неподвижных полутоновых видеоизображений каждому пикселу k неподвижных полутоновых видеоизображений присваивают значение соответствующего элемента k матриц восстановленных квантованных отсчетов неподвижных полутоновых видеоизображений размером М×М элементов.An identical normalization matrix of size N × N elements is generated on the receiving and transmitting sides, the elements of which C (i, j) are calculated by the formula

where i = 1, 2, ..., N, j = 1, 2, ..., N. As a random rectangular matrix of size mxN elements, a transposed random rectangular matrix of size N × m elements is received on the transmitting side. K Matrices of coefficients of a two-dimensional discrete cosine transform of M × M elements are formed by sequentially multiplying a matrix of a discrete cosine transform of M × M elements by each matrix of quantized samples of a still grayscale video image of M × M elements and by a transposed discrete cosine transform matrix of size M × M elements. Then, k matrices of coefficients of a two-dimensional discrete cosine transform of size N × N elements are formed, according to the formula A _g (i, j) = L _g (i, j), where i = 1, 2, ..., N, j = 1 , 2, ..., N, g = 1, 2, ..., k, Lg (i, j) -i, the jth element of the gth matrix of coefficients of a two-dimensional discrete cosine transform of size M × M elements, Ag (i, j) -i, jth element of the gth matrix of coefficients of a two-dimensional discrete cosine transform of size N × N elements, with N <M selected. Then, k matrices of normalized values of N × N elements are formed by multiplying each coefficient of the matrix of coefficients of a two-dimensional discrete cosine transform of N × N elements of size A _g (I, j) by the corresponding element of the normalization matrix of N × N elements. Each of the key matrices of sizes N × m and m × N elements is added modulo 2, respectively, with a direct and transposed random rectangular matrix of sizes N × m and m × N elements, and after calculating the standard error between the corresponding elements of each resulting matrix of size N × N elements and matrices of normalized values of size N × N elements, calculate their total amount. After inverting each element of a random rectangular matrix of size N × m, the resulting total amount is compared with the previous total amount. A random rectangular matrix of N × m elements in size is transmitted via the communication channel, and on the receiving side, after multiplying k random N × m matrices by a random × m × m matrix, the resulting matrices of N × N elements are transformed into k random matrices of size m × N by elementwise dividing their elements into the corresponding elements of the normalization matrix of size N × N elements. The resulting k matrices of reconstructed coefficients with sizes of N × N elements are supplemented with zeros to sizes M × M of elements. K matrices of fixed grayscale images are restored by sequentially multiplying the transposed matrix of a discrete cosine transform of size M × M elements by k matrices of reconstructed coefficients of a two-dimensional discrete cosine transform of size M × M elements and by a matrix of discrete cosine transformation of size M × M elements. To form k matrices of quantized samples of a stationary grayscale video image with dimensions M × M elements, each element S _g (x, y), where x = 1, 2, ..., M, y = 1, 2, ..., M, g = 1, 2, ..., k, is assigned the quantized value of the corresponding pixel g of still halftone video images of size N × N. To represent k matrices of quantized samples of a stationary halftone video image of size M × M elements in the form of k stationary halftone video images, each pixel k of stationary halftone video images is assigned the value of the corresponding element of k matrices of reconstructed quantized samples of stationary halftone video images of size M × M elements.

The prototype method allows, without compromising the quality of message recovery, to increase the speed of information transfer to a value at which it is possible to conduct video-information exchange via low-speed digital communication channels.

The disadvantage of this prototype method is the relatively low resistance to errors in the digital communication channel. This is due to the fact that on the receiving side, digital sequences are considered received without errors, therefore, when the characters in the transmitted digital sequences are inverted, the messages will be restored with certain distortions due to the instability of the communication channel parameters.

The aim of the invention is to develop a method of compression and restoration of messages, providing increased resistance to errors in the digital communication channel during compression and restoration of messages.

где i=1, 2, ..., N, j=1, 2, ..., N, и формируют матрицу квантованных отсчетов неподвижного полутонового видеоизображения размером М×М элементов, в которой каждому ее элементу S(x,y) присваивают квантованное значение соответствующего пиксела неподвижного полутонового видеоизображения, размером М×М пикселов, где x=1, 2, ..., M; y=1, 2, ..., M. Далее формируют матрицу коэффициентов двумерного дискретно-косинусного преобразования размером М×М элементов путем последовательного перемножения матрицы дискретно-косинусного преобразования размером М×М элементов на матрицу квантованных отсчетов неподвижного полутонового видеоизображения размером М×М элементов и на транспонированную матрицу дискретно-косинусного преобразования размером М×М элементов. Формируют матрицу коэффициентов двумерного дискретно-косинусного преобразования размером N×N элементов, по формуле A(i,j)=L(i,j), где L(ij)-i,j-й элемент матрицы коэффициентов двумерного дискретного косинусного преобразования размером M×M элементов, A(i,j)-I, j-й элемент матрицы коэффициентов двумерного дискретно-косинусного преобразования размером N×N элементов, причем выбирают N<M, после чего формируют матрицу нормированных значений размером N×N элементов путем умножения каждого коэффициента матрицы коэффициентов двумерного дискретно-косинусного преобразования размером N×N элементов А(i,j) на соответствующий ему элемент нормировочной матрицы размером N×N элементов. Затем генерируют случайную прямоугольную матрицу размером N×m элементов, а в качестве случайной прямоугольной матрицы размером m×N элементов принимают транспонированную случайную прямоугольную матрицу размером N×m элементов, затем каждую из ключевых матриц размерами N×m и m×n элементов суммируют по модулю 2 соответственно с прямой и транспонированной случайной прямоугольной матрицей размерами N×m и m×N элементов. Преобразуют полученные матрицы путем деления элементов каждой строки случайной прямоугольной матрицы размером N×m элементов на сумму единиц соответствующей строки и деления элементов каждого столбца случайной прямоугольной матрицы размером m×N элементов на сумму единиц соответствующего столбца. Далее вычисляют k результирующих матриц V(g), где g=1, 2, ..., k, размером N×N элементов путем последовательного умножения k преобразованных случайных прямоугольных матриц размером N×m на случайную квадратную матрицу размером m×m и на k преобразованных случайных прямоугольных матриц размером m×N элементов. Последовательно инвертируют каждый элемент случайных прямоугольных матриц размерами N×m и m×N элементов и после инверсии преобразуют их путем деления элементов каждой строки случайной прямоугольной матрицы с инвертированным элементом размером N×m элементов на сумму единиц соответствующей строки и деления элементов каждого столбца случайной прямоугольной матрицы с инвертированным элементом размером m×N элементов на сумму единиц соответствующего столбца. Повторно вычисляют k результирующих матриц размером N×N элементов, путем последовательного умножения k преобразованных случайных прямоугольных матриц с инвертированным элементом размером N×m на случайную квадратную матрицу размером m×m и на k преобразованных случайных прямоугольных матриц с инвертированным элементом размером m×N. Передают по каналу связи случайную прямоугольную матрицу размером N×m и принимают из канала связи эту матрицу. Затем каждую из ключевых матриц размерами N×m и m×N элементов суммируют по модулю 2 соответственно с прямой и транспонированной случайными прямоугольными матрицами размерами N×m и m×N элементов. Преобразуют принятые случайные прямоугольные матрицы размерами N×m и m×N путем деления элементов строки каждой случайной прямоугольной матрицы размером N×m элементов на сумму единиц соответствующей строки и деления элементов каждого столбца случайной прямоугольной матрицы размером m×N элементов на сумму единиц соответствующего столбца. Затем вычисляют k восстановленных результирующих матриц

где g=1, 2, ..., k, размером N×N элементов путем последовательного умножения k преобразованных случайных прямоугольных матриц размером N×m на случайную квадратную матрицу размером m×m и на k преобразованных случайных прямоугольных матриц размером m×N соответственно, а матрицу восстановленных коэффициентов размером N×N элементов дополняют нулями до размеров М×М элементов. Получают матрицу восстановленных коэффициентов дискретно-косинусного преобразования размером М×М элементов, восстанавливают матрицу неподвижного полутонового изображения путем последовательного перемножения транспонированной матрицы дискретно-косинусного преобразования размером М×М элементов на матрицу восстановленных коэффициентов двумерного дискретно-косинусного преобразования размером М×М элементов и на матрицу дискретно-косинусного преобразования размером М×М элементов. Формируют цифровой информационный сигнал, каждому пикселу неподвижного полутонового видеоизображения присваивают значение соответствующего элемента матрицы восстановленных квантованных отсчетов неподвижных полутоновых видеоизображений размером М×М элементов. После вычисления k результирующих матриц вычисляют суммарную матрицу размером N×N элементов V_s по формуле

Затем вычисляют среднеквадратическую ошибку между элементами матрицы нормированных значений размером N×N элементов и элементами суммарной матрицы V_s размером N×N элементов. После инверсии каждого элемента случайных прямоугольных матриц размерами N×m и m×N повторно вычисляют k результирующих матриц, суммарную матрицу V_s и среднеквадратическую ошибку между элементами матрицы нормированных значений размером N×N элементов и элементами повторно вычисленной суммарной матрицы V_s размером N×N элементов. Полученную среднеквадратическую ошибку вычитают от предыдущей среднеквадратической ошибки и в случае положительной разности запоминают инвертированный элемент, а после вычисления k восстановленных результирующих матриц

вычисляют восстановленную суммарную матрицу размером N×N элементов

_s по формуле

а для получения матрицы восстановленных коэффициентов размером N×N элементов преобразуют восстановленную суммарную матрицу размером N×N элементов путем поэлементного деления ее элементов на соответствующие элементы нормировочной матрицы размером N×N элементов.This goal is achieved by the fact that in the known method of compressing and recovering messages, a random square matrix of size m × m elements, each element of which belongs to the range of -500 ÷ +500, is preliminarily generated on the transmitting and receiving sides. Generate k random key matrices of size N × m and m × N elements. Then a normalization matrix is formed with the size of N × N elements, the elements of which C (i, j) are calculated by the formula

where i = 1, 2, ..., N, j = 1, 2, ..., N, and form a matrix of quantized samples of a fixed grayscale video image with the size of M × M elements, in which each of its elements S (x, y) assign the quantized value of the corresponding pixel of a stationary grayscale video image, the size of M × M pixels, where x = 1, 2, ..., M; y = 1, 2, ..., M. Next, a matrix of coefficients of a two-dimensional discrete cosine transform of size M × M elements is formed by sequentially multiplying a matrix of discrete cosine transforms of size M × M elements by a matrix of quantized samples of a still halftone video image of size M × M elements and on the transposed matrix of discrete cosine transform size M × M elements. The matrix of coefficients of a two-dimensional discrete cosine transform of size N × N elements is formed, according to the formula A (i, j) = L (i, j), where L (ij) -i, the jth element of the matrix of coefficients of a two-dimensional discrete cosine transform of size M × M elements, A (i, j) -I, j-th element of the matrix of coefficients of a two-dimensional discrete cosine transform of size N × N elements, moreover, select N <M, and then form a matrix of normalized values of size N × N elements by multiplying each the coefficient matrix of the coefficients of a two-dimensional discrete cosine transforming the size of N × N elements A (i, j) to the corresponding element of the normalization matrix of size N × N elements. Then a random rectangular matrix of size N × m elements is generated, and a transposed random rectangular matrix of size N × m elements is taken as a random rectangular matrix of size m × N, then each of the key matrices of size N × m and m × n elements is summed modulo 2, respectively, with a direct and transposed random rectangular matrix of sizes N × m and m × N elements. The resulting matrices are transformed by dividing the elements of each row of a random rectangular matrix of size N × m elements by the sum of units of the corresponding row and dividing the elements of each column of a random rectangular matrix of size m × N elements by the sum of units of the corresponding column. Next, k resulting matrices V (g) are calculated, where g = 1, 2, ..., k, of size N × N elements by successively multiplying k transformed random rectangular matrices of size N × m by a random square matrix of size m × m and by k transformed random rectangular matrices of size m × N elements. Each element of random rectangular matrices with sizes of N × m and m × N elements is sequentially inverted and, after inversion, they are converted by dividing the elements of each row of a random rectangular matrix with an inverted element of size N × m elements by the sum of the units of the corresponding row and dividing the elements of each column of the random rectangular matrix with an inverted element of size m × N elements in the sum of units of the corresponding column. Recalculate k resultant matrices of size N × N elements by sequentially multiplying k transformed random rectangular matrices with an inverted element of size N × m by a random square matrix of size m × m and k converted random rectangular matrices with an inverted element of size m × N. A random rectangular N × m matrix is transmitted via the communication channel and this matrix is received from the communication channel. Then, each of the key matrices of sizes N × m and m × N elements is added modulo 2, respectively, with direct and transposed random rectangular matrices of sizes N × m and m × N elements. Accepted random rectangular matrices of sizes N × m and m × N are converted by dividing the row elements of each random rectangular matrix of size N × m elements by the sum of units of the corresponding row and dividing the elements of each column of a random rectangular matrix of size m × N elements by the sum of units of the corresponding column. Then, k reconstructed result matrices are calculated.

where g = 1, 2, ..., k, by the size of N × N elements by sequentially multiplying k transformed random rectangular matrices of size N × m by a random square matrix of size m × m and by k converted random rectangular matrices of size m × N, respectively and the matrix of reconstructed coefficients with the size of N × N elements is supplemented with zeros to the sizes of M × M elements. A matrix of reconstructed coefficients of a discrete cosine transform of M × M elements is obtained, a matrix of a fixed grayscale image is restored by sequentially multiplying a transposed matrix of a discrete cosine transform of M × M elements by a matrix of reconstructed coefficients of a two-dimensional discrete cosine transform of M × M elements and a matrix discrete cosine transform of size M × M elements. A digital information signal is generated, each pixel of a stationary grayscale video image is assigned a value of the corresponding element of the matrix of reconstructed quantized samples of stationary grayscale video images of size M × M elements. After calculating the k resulting matrices, a total matrix of size N × N elements V _{s is} calculated by the formula

Then calculate the standard error between the elements of the matrix of normalized values of size N × N elements and the elements of the total matrix V _{s of} size N × N elements. After inverting each element of random rectangular matrices of sizes N × m and m × N, k resulting matrices, the total matrix V _s and the standard error between the elements of the normalized value matrix of N × N elements and the elements of the recalculated total matrix V _{s of} size N × N are recalculated elements. The resulting mean square error is subtracted from the previous mean square error and, in the case of a positive difference, the inverted element is stored, and after calculating k reconstructed resulting matrices

calculate the reconstructed total matrix of size N × N elements

_s by the formula

and to obtain a matrix of reconstructed coefficients of size N × N elements, the reconstructed total matrix of size N × N elements is converted by elementwise division of its elements into corresponding elements of a normalization matrix of size N × N elements.

Thanks to the new set of essential features, due to the discrete cosine transform performed over the matrix of quantized samples of a fixed grayscale video image, the transition to the video representation in the form of a matrix of coefficients of a two-dimensional discrete cosine transform is provided. To reduce the digital presentation of the video image, not all DCT coefficients are encoded and transmitted, but only N ² DCT coefficients from the spectral region with maximum energy, and to increase error resistance in the digital communication channel, the compensation of errors that occur in the digital communication channel is based on the summation and averaging k resulting matrices. The aforementioned provides error tolerance during compression and restoration of a message, thereby improving the quality of message recovery during transmission over the communication channel with errors.

The analysis of the prior art made it possible to establish that analogues that are characterized by a combination of features that are identical to all the features of the claimed technical solution are absent, which indicates the compliance of the claimed method with the condition of patentability "novelty".

Search results for known solutions in this and related fields of technology in order to identify features that match the distinctive features of the prototype of the claimed method showed that they do not follow explicitly from the prior art. The prior art also did not reveal the popularity of the impact provided by the essential features of the claimed invention, the transformations on the achievement of the specified technical result. Therefore, the claimed invention meets the condition of patentability "inventive step".

The claimed method is illustrated by drawings.

- Figa. Formation of a random square matrix of size m × m elements.

- Fig.1b. A variant of a random square matrix of size m × m elements.

- Figure 2. Formation of a matrix of coefficients of a two-dimensional discrete cosine transform with the size of M × M elements.

- Figure 3. Formation of a matrix of coefficients of a two-dimensional discrete cosine transform of size N × N elements.

- Figa, 4b. Formation of a normalization matrix of size N × N elements.

- Figure 5. Formation of a matrix of normalized values of size N × N elements.

- Figa. Generation of k random key matrices of size Nxm elements.

- Fig.6b. Variant of k random key matrices of size N × m elements.

- Fig.6c. Generation of k random key matrices of size m × N elements.

- Fig.6g. Variant of k random key matrices of size m × N elements.

- Fig 7a. Formation of a random rectangular matrix of size N × m elements.

- Fig.7b. A variant of a random rectangular matrix of size N × m elements.

- Figv. Formation of k random rectangular matrices of size N × m elements.

- Fig 7g. Formation of k random rectangular matrices of size m × N elements.

- Fig.7d. Convert k random rectangular matrices of size N × m elements.

- Fig. 7e. Transformation of k random rectangular matrices of size m × N elements.

- Fig. 8. Formation of k resulting matrices of size N × N elements.

- Figa. Variant of inversion of an element of a random rectangular matrix of size N × m elements.

- Figure 10. Transmission of a random rectangular matrix of size N × m elements over a digital communication channel.

- Figa. A variant of the matrix of coefficients of a two-dimensional discrete cosine transform with the size of M × M elements.

- Fig. 11b. Graph of the absolute values of the first row of the matrix of coefficients of a two-dimensional discrete cosine transform with the size of M × M elements.

- Fig. 12. Formation of a matrix of reconstructed coefficients of a two-dimensional discrete cosine transform of size N × N elements.

- Fig.13. Formation of a matrix of reconstructed coefficients of a two-dimensional discrete cosine transform with the size of M × M elements.

- Fig. 14. Formation of a matrix of reconstructed quantized samples of a stationary grayscale video image.

The ability to implement the claimed method of compression and recovery of messages is explained as follows. If it is necessary to transmit over a communication channel a message whose volume exceeds the capabilities of a communication channel or for transmitting which an unacceptably large time interval is required, various methods are used to reduce the amount of transmitted message.

For example, (see the book: W. Prett. Digital image processing. Part 1. - M .: Mir, 1982, p.96-118) the encoded message is represented as the product of the matrix of support vectors by the matrix of decomposition coefficients. For this purpose, one of the well-known techniques is used: the discrete cosine transform, the fast Fourier transform, the Karunen-Loeve transform, the wavelet transform, and others.

This technique causes a certain decrease in the amount of information necessary for transmission over the communication channel and at the same time achieve the required quality.

At the receiving end, the received message is restored.

Thus, with some deterioration in the quality of the transmitted information, they provide a decrease in the amount of information necessary for transmission. At the same time, the amount of transmitted information about the matrix of support vectors and the matrix of decomposition coefficients is still large, which does not meet the requirements for modern communication channels while maintaining the required quality, and these techniques do not provide error tolerance in the communication channel. To increase error tolerance in the communication channel, noise-resistant coding is used, described, for example, in the book: W. Peterson, E. Weldon. Error correction codes. - M .: Mir, 1976. This error-correcting coding is based on the division of all possible code combinations into allowed and forbidden. This approach involves the introduction of redundancy in a transmitted digital sequence. This leads to a significant reduction in the degree of compression of the transmitted information and, accordingly, an increase in the requirements for the transmission speed of the digital communication channel. There is also a known method of controlling interference based on the accumulation method, described, for example, in the book: A.A. Kharkevich. Fighting interference. - M.: GIFFL, 1963. This method is based on the transmission of a single message through several independent channels. This method increases the signal-to-noise ratio by a factor of k without increasing the signal power. However, for this gain you have to pay with k multiple use of the channel. With time division of channels, the transmission time increases by a factor of k, and with a frequency division, the occupied frequency band by a factor of k, etc.

The proposed method solves the problem of reducing the amount of transmitted data and ensuring the stability of the restored images to the influence of errors based on the accumulation method with a single use of the channel.

The proposed method is implemented as follows.

Formation on the transmitting and receiving sides of a random square matrix of size m × m elements (hereinafter, denote it as [B] _{m × m} ), each element of which belongs to the range -500 ÷ +500 (see figa, 1b). The size m of the matrix [B] _{m × m is} chosen empirically based on the size of the transmitted message - M. Experimental studies show that for a qualitative approximation of the transmitted message, the size m is 1 / 5-1 / 4 of the size of the transmitted message. The operation of forming the matrix [B] _{m × m} can be performed using a random number sensor. To fulfill the identity requirement of the receiver matrix [B] _{m × m to} a similar transmitter matrix, elements of the matrix [B] _{m × m} can be generated on the transmitting side and transmitted via a digital communication channel to the receiving side, for example, as part of a sync packet.

As a message to be compressed and restored, a stationary halftone video image is considered from which a matrix of quantized samples of a stationary halftone video image of size M × M elements is formed, assigning to each of its elements S (x, y), where x = 1, 2, .. ., M; y = 1, 2, ..., M, the quantized value of the corresponding pixel of a stationary grayscale video image (see Fig. 15).

In order to reduce the amount of information transmitted over the communication channel, a discrete cosine transform is used, described, for example, in the book: N. Ahmed, K. R. Rao. Orthogonal transformations when processing digital signals. - M .: Communication, 1980, p. 156-159.

The matrix of coefficients of a two-dimensional discrete cosine transform of size M × M elements is formed based on the expression

[L (x, y)] _{M × M} = [G ([x, y)] _{M × M} × [S (x, y)] _{M × M} , ([G (x, y) _{M × M} , where [L (x, y)] _{M × M} is the matrix of coefficients of a two-dimensional discrete cosine transform of a stationary halftone video image of size M × M elements, [S (x, y)] _{M × M} is a matrix of quantized samples of a stationary halftone video image of size M × M elements, [G (x, y)] _{M × M} is the matrix of the direct discrete cosine transform, [G (x, y)] ' _{M × M} is the matrix of the inverse discrete cosine transform (see FIG. 2).

The most informative, from the point of view of restoring the transmitted video image, are the coefficients of the two-dimensional discrete cosine transform with maximum energy, located in the upper left quadrant of the matrix of coefficients of the two-dimensional discrete cosine transform with the size of M × M elements (see Fig. 11a). They are distinguished by forming a matrix of coefficients of a two-dimensional discrete cosine transform of size N × N elements (hereinafter, denote it as [A] _{N × N} ), based on the expression A (i, j) = L (i, j), where i = 1, 2, ..., N, j = 1, 2, ..., N, L (i, j) -i, the jth element of the coefficient matrix of a two-dimensional discrete cosine transform of a stationary grayscale video image of size M × M elements, A (i, j) -i, jth element of the matrix of coefficients of a two-dimensional discrete-cosine transform of a stationary grayscale video image of size N × N elements, and N≤M (s m. figure 3).

(см. фиг.4), полученную опытным путем. При этом учтена особенность матрицы коэффициентов двумерного дискретно-косинусного преобразования размером М×М элементов, заключающаяся в расположении коэффициентов с максимальной энергией в левом верхнем квадранте и зависимости значений коэффициентов от их порядкового номера (i и j).The magnitude of the coefficients of the two-dimensional discrete cosine transform depends to a large extent on their serial number, which can be judged from the graph (see Fig. 11b), where the ordinal numbers of the coefficients of the first row of the coefficient matrix of the two-dimensional discrete cosine transform of size M are plotted on the abscissa × M elements, and their absolute values along the ordinate axis. In order to eliminate the dependence of the magnitude of the matrix elements of the coefficients of the two-dimensional discrete cosine transform of size N × N elements on their location in the matrix and to approximate them more accurately in the future, it is necessary to carry out the normalization operation. The essence of this operation is that on the transmitting and receiving sides, a normalization matrix of size N × N elements is identical formed (hereinafter, denote it as [C] _{N × N} ), the elements of which C (i, j) are calculated by the formula

(see figure 4) obtained experimentally. In this case, the peculiarity of the coefficient matrix of the two-dimensional discrete cosine transform with the size of M × M elements was taken into account, consisting in the arrangement of the coefficients with maximum energy in the upper left quadrant and the dependence of the coefficient values on their serial number (i and j).

Then, a matrix of normalized values of the two-dimensional discrete cosine transform of size N × N elements (hereinafter, referred to as [V] _{N × N} ) is formed by multiplying each element A (i, j) of the coefficient matrix of the two-dimensional discrete cosine transform of a fixed grayscale video image of size N × N elements to the corresponding element C (i, j) of the normalization matrix of size N × N elements (see figure 5).

) в виде произведения трех матриц: преобразованной прямоугольной матрицы размером N×m элементов (в дальнейшем обозначим ее как

), случайной квадратной матрицы размером m×m элементов [B]_m×m и преобразованной прямоугольной матрицы размером m×N элементов (в дальнейшем обозначим ее как

) (см. фиг.8):

где [Y_pr(g)] и [X_pr(g)] находятся таким образом, чтобы суммарная матрица размером N×N элементов (в дальнейшем обозначим ее как [V_s]_N×N) полученная путем суммирования соответствующих элементов всех матриц

и деления на k, была наиболее близкой по заданному критерию к матрице [V]_N×N.Further, similarly to the prototype method, an approach based on the representation of the gth - resulting matrix of size NxN elements is used (hereinafter, we denote it as

) in the form of the product of three matrices: a transformed rectangular matrix of size N × m elements (hereinafter, denote it as

), a random square matrix of size m × m elements [B] _{m × m,} and a transformed rectangular matrix of size m × N elements (hereinafter, denote it as

) (see Fig. 8):

where [Y _pr (g)] and [X _pr (g)] are found so that the total matrix of size N × N elements (hereinafter, denote it as [V _s ] _{N × N} ) obtained by summing the corresponding elements of all matrices

and dividing by k, was closest according to a given criterion to the matrix [V] _{N × N.}

и

формируют путем суммирования по модулю 2 случайной прямоугольной матрицы [Е]_N×m со случайной ключевой матрицей [Y_кл(g)]_N×m и транспонированной прямоугольной матрицы [Е]^T _N×m со случайной ключевой матрицей [X_кл(g)]_m×N соответственно, где матрицы [Y_кл(g)]_N×m и [X_кл(g)]_m×N являются идентично генерируемыми на передающей и приемной сторонах размерами N×m и m×N соответственно (см. фиг.7в, 7 г), где знак

означает суммирование по модулю 2.Matrices

and

form by summing modulo 2 a random rectangular matrix [E] _{N × m} with a random key matrix [Y _cells (g)] _{N × m} and a transposed rectangular matrix [E] ^T _{N × m} with a random key matrix [X _cells (g) ] _{m × N,} respectively, where the matrices [Y _cells (g)] _{N × m} and [X _cells (g)] _{m × N} are identically generated on the transmitting and receiving sides with sizes N × m and m × N, respectively (see FIG. .7c, 7d), where the sign

means summation modulo 2.

и

является то, что они могут быть легко приведены к цифровому виду. Это достигается тем, что на элементы этих матриц накладываются следующие ограничения:Matrix feature

and

is that they can be easily digitized. This is achieved by the following restrictions on the elements of these matrices:

и

принимают значения в диапазоне от нуля до единицы;- matrix elements

and

take values in the range from zero to one;

равны между собой и в сумме образуют единицу;- nonzero elements of each row of the matrix

are equal to each other and in total form a unit;

равны между собой и в сумме образуют единицу;- nonzero elements of each column of the matrix

are equal to each other and in total form a unit;

умножить на количество ненулевых элементов в этой строке, то будет получена матрица [Y_pr(g)]_N×m элементы которой определены только на множестве "1" и "0". Аналогично, если элементы каждого столбца матрицы

умножить на количество ненулевых элементов в столбце, то будет получена матрица [X_pr(g)]_m×N элементы которой определены только на множестве "1" и "0".Under such restrictions, if the elements of each row of the matrix

multiplied by the number of non-zero elements in this row, the matrix will be obtained [Y _pr (g)] _{N × m} whose elements are defined only on the set "1" and "0". Similarly, if the elements of each column of the matrix

multiplied by the number of nonzero elements in the column, the matrix will be obtained [X _pr (g)] _{m × N} whose elements are defined only on the set "1" and "0".

и

подробно описана в способе-прототипе (см. патент РФ №2244963, МПК⁷ Н 04 N 7/30, от 2005 г.).A procedure that implements a search on the transmitting side of optimal matrices

and

described in detail in the prototype method (see RF patent No. 2244963, IPC ⁷ H 04 N 7/30, from 2005).

и

(см. фиг.7д, 7е).Thus, the representation of the matrix of normalized values of a two-dimensional discrete cosine transform size N × N elements [V] _{N × N} in digital form on the transmission side is carried out based on generating a plurality of zero and unit cells in the form of a random rectangular matrix of size N × m (matrix [ E] _{N × N} ) ( ^{see Figs} . 7a, 7b) and k random key matrices of size m × N and N × m elements (matrices [X _cells (g)] and [Y _cells (g)] _{N × m} ( cm. 6b, 6d) is then random rectangular matrix _{[X (g) m × N} ] and _{[Y (g)] N ×} m is converted by dividing elements of each row cases hydrochloric rectangular matrix of size N × m elements in the amount corresponding row units, i.e. its weight - v _y (g) (see the book: E. Berlekamp, Algebraic Coding Theory - M .: Mir, 1971, p.12... ) (see Fig.7d) and dividing the elements of each column of a random rectangular matrix of size m × N elements by the sum of the units of the corresponding column, i.e., its weight is v _x (g).

and

(see fig.7d, 7e).

путем последовательного перемножения полученной после преобразования прямоугольной матрицы размером N×m элементов

случайной квадратной матрицы размером m×m элементов [B]_m×m и полученной после преобразования прямоугольной матрицы размером m×N элементов

(см. фиг.8).Similarly to the prototype method, k resulting matrices of size N × N elements are calculated, i.e.

by successively multiplying the obtained after the transformation of a rectangular matrix of size N × m elements

random square matrix of size m × m elements [B] _{m × m} and obtained after the transformation of a rectangular matrix of size m × N elements

(see Fig. 8).

где

- i,j - элемент g-й результирующей матрицы.Next, the resulting resulting matrices are summarized according to the rule

Where

- i, j is the element of the gth resulting matrix.

размером N×N элементов поэлементно суммируют и усредняют по формуле

The matrix [V _s ] _{N × N} should be closest to the matrix [V] _{N × N} by some criterion. It is known (see, for example, the book: W. Prett. Digital image processing. Part I. - M .: Mir, 1982, p. 121-127) that one of the main objective criteria for proximity is the standard error. By minimizing the standard error, the minimum discrepancies between the matrices [V] _{N × N} and [V _s ] _{N × N} are achieved. Therefore, the sum of the squared differences between the elements of the total resulting matrix of size N × N elements [V _s ] _{N × N} and the corresponding elements of the matrix of normalized two-dimensional discrete-cosine transforms of size N × N elements [V] _{N × N is calculated} . Then each element of a random rectangular matrix of size N × m elements is sequentially inverted (see Fig. 9) and they are transformed in the same way as described when transforming the matrices [Y (g)] _{N × m} and [X (g)] _{m × N} (see Fig. 7b, 7c, 7d, 7d, 7e). Sequentially multiply k random rectangular matrices of size Nxm elements obtained after conversion, multiply a random square matrix of size m × m elements and obtained after conversion of k random rectangular matrices of size m × N elements. The resulting k resulting matrices

the size of N × N elements are element-wise summed and averaged according to the formula

и

изменятся значения элементов результирующей матрицы

тем самым изменяя значения матрицы

Затем для оценки степени приближения матрицы

к [V]_N×N повторно рассчитывают сумму квадратов разностей между элементами суммарной результирующей матрицы размером N×N элементов и элементами матрицы нормированных значений двумерного дискретно-косинусного преобразования размером N×N элементов. Затем вычитают полученную сумму квадратов разности от аналогичной суммы, полученной на предыдущем шаге. В случае положительной разности, т.е. уменьшения среднеквадратической ошибки, сохраняют инвертированное значение элемента, а в противном случае - выполняют его повторную инверсию.Since the matrix [E] _{N × m} contained an inverted element, which after conversion led to a change in the values of the elements of the matrices [Y (g)] _{N × m} and [X (g)] _{m × N} and, accordingly, led to changes in the matrices

and

the values of the elements of the resulting matrix will change

thereby changing the values of the matrix

Then, to estimate the degree of approximation of the matrix

to [V] _{N × N, the} sum of the squared differences between the elements of the total resulting matrix of N × N elements and the elements of the normalized values of the two-dimensional discrete cosine transform of N × N elements is recalculated. Then, the resulting sum of the squares of the difference is subtracted from the similar amount obtained in the previous step. In the case of a positive difference, i.e. reduce the standard error, save the inverted value of the element, and otherwise, perform its repeated inversion.

и [V]_N×N, что однозначно указывает на оптимальность сформированных матриц [Y(g)] _N×m, [X(g)]_m×N и

и

т.e. достижение наилучшего качества при заданном фиксированном объеме передаваемой информации.Similarly, invert all the bits into the matrices [E] _{N × m} and achieve the minimum mean square error between the matrices

and [V] _{N × N} , which uniquely indicates the optimality of the generated matrices [Y (g)] _{N × m} , [X (g)] _{m × N} and

and

i.e. achieving the best quality for a given fixed amount of information transmitted.

A plurality of zero and single elements of a random rectangular matrix [E] _{N × m} is transmitted over a communication channel (see Fig. 10). In figure 10, the symbol · denotes the multiplication of matrices.

и

At the receiving side, a plurality of zero and single elements of a random rectangular matrix [E] _{N × m is} received from the communication channel. Then, the matrices [Y (g)] _{N × m} and [X (g)] _{m × N} are calculated by summing modulo 2 the matrices [E] _{N × m} onto the matrix [Y _cells (g)] _{N × m} and summing modulo 2 transposed matrices [E] _{N × m} per matrix [X _cells (g)] _{m × N,} respectively. Then, the matrices [Y (g)] _{N × m} and [X (g)] _{m × N are} transformed by dividing the elements of each row of a rectangular matrix of size N × m elements by the sum of the units of the corresponding row, i.e. its weight v _y (see FIG. 7e) and the division of the elements of each column of a rectangular matrix of size m × N elements by the sum of the units of the corresponding column, i.e. its weight v _x (see fig.7d). Thus, matrices are formed on the receiving side

and

путем последовательного перемножения k случайных прямоугольных матриц

случайной квадратной матрицы [B]_m×m и k случайных прямоугольных матрицы

(см. фиг.8). Затем формируют матрицу восстановленных нормированных значений двумерного дискретно-косинусного преобразования размером N×N элементов

путем суммирования и усреднения k матриц восстановленных результирующих матриц размером N×N элементов

по формуле

Form k reconstructed resultant matrices of size N × N elements

by successively multiplying k random rectangular matrices

random square matrix [B] _{m × m} and k random rectangular matrices

(see Fig. 8). Then, a matrix of reconstructed normalized values of the two-dimensional discrete cosine transform with the size of N × N elements is formed

by summing and averaging k matrices of the restored resulting matrices of size N × N elements

according to the formula

_M×M) формируют путем деления значения каждого i,j-го элемента матрицы

на соответствующий элемент нормировочной матрицы размером N×N элементов (см. фиг.12).To obtain the restored coefficients of the real dimension, it is necessary to perform the denormation operation. Considering that on the receiving side, a normalization matrix [C] _{N × N} , a matrix of reconstructed values of a two-dimensional discrete cosine transform of size N × N elements (in the future, we denote it as

_{M × M} ) is formed by dividing the values of each i, jth matrix element

on the corresponding element of the normalization matrix of size N × N elements (see Fig. 12).

). Эту операцию производят путем присвоения значения каждого i,j-го элемента матрицы восстановленных коэффициентов двумерного дискретно-косинусного преобразования размером N×N элементов каждому i,j-му элементу матрицы восстановленных коэффициентов двумерного дискретно-косинусного преобразования размером М×М элементов, а в качестве остальных элементов записывают нули (см. фиг.13).To restore the transmitted message, it is necessary to form a matrix of the reconstructed coefficients of the two-dimensional discrete cosine transform with the size of M × M elements (hereinafter, denote it as

) This operation is performed by assigning the value of each i, jth element of the matrix of reconstructed coefficients of a two-dimensional discrete cosine transform of size N × N elements to each i, jth element of the matrix of reconstructed coefficients of a two-dimensional discrete cosine transform of size M × M elements, and as the remaining elements record zeros (see Fig.13).

(х,y)]_M×M=[Г(x,у)]'_M×M×[

(x,y)]_M×M×[Г(x,y)]_M×M, где

- матрица восстановленных квантованных отсчетов неподвижного полутонового видеоизображения размером МхМ элементов.Next, a matrix of reconstructed quantized samples of a fixed grayscale video image is formed by multiplying the transposed matrix of a discrete cosine transform of size M × M elements by a matrix of reconstructed coefficients of a two-dimensional discrete cosine transform of size M × M elements and a matrix of discrete cosine transform of size M × M elements (cm Fig. 14), i.e. based on the formula: [

(x, y)] _{M × M} = [G (x, y)] ' _{M × M} × [

(x, y)] _{M × M} × [G (x, y)] _{M × M} , where

- a matrix of reconstructed quantized samples of a stationary grayscale video image with the size of MXM elements.

в виде неподвижного полутонового видеоизображения, присвоив каждому пикселу неподвижного полутонового видеоизображения значение соответствующего элемента матрицы

At the last stage, they present the matrix

in the form of a motionless grayscale video image, assigning to each pixel of a motionless grayscale video image the value of the corresponding matrix element

To assess the feasibility of achieving the formulated technical result when using the claimed method for compressing and recovering messages, simulation was carried out on a PC. The size of the random square matrix [B] _{m × m} was 128 × 128 elements. This matrix size [B] _{m × m is} selected based on the fact that a stationary halftone video image of 512 × 512 pixels is used as the initial message. In the proposed method, a high degree of compression of the original message is achieved due to the fact that in order to form a stationary grayscale video image on the receiving side, it is necessary to transmit the number of binary units determined by the size of the matrix [E] _{N × m} to the digital communication channel. To increase the noise immunity, an approach was used that

based on the accumulation method, error compensation was carried out by summing and averaging k images of the recovered message, which were formed on the basis of random random-independent key matrices known on the transmitting and receiving sides k and one matrix [E] _{N × m} obtained from the communication channel, thus the method accumulation was implemented without multiple transmission of the matrix [E] _{N × m} . In the general case, the matrix [E] _{N × m} is rectangular. But in the course of simulation N is taken equal to 128, and m = 128. This value of N is due to the quality requirements of the reconstructed video image. Practical studies show that when 1/16 of the spectral coefficients of the two-dimensional discrete cosine transform are left from the upper left quadrant of the matrix of two-dimensional discrete cosine transform coefficients with a size of 512 × 512 elements, the peak signal-to-noise ratio for the original and reconstructed video image is about 30 dB. During simulation, the parameter number k was chosen experimentally, k = 12, a decrease in this parameter leads to a sharp decrease in the error compensation value. With an increase in this parameter, the gain increases slightly, but the quality of restoring a stationary grayscale image decreases.

The achieved compression ratio can be found by the formula:

The number 8 in the numerator of this formula indicates that for encoding directly a stationary grayscale video image, i.e. the value of each pixel lies in the range 0 ÷ 255, 8 bits are required. When choosing N = 128, m = 128 and M = 512, the resulting compression ratio was 16 times. When using the prototype method for compressing messages, the resulting compression ratio was 16 times with a peak signal-to-noise ratio of about 29.5 dB, but when simulating errors in the communication channel, the recovery quality was 16 dB. An objective assessment of the quality of the video image restored using the claimed method shows that the peak signal-to-noise ratio for the original and restored video images is 28.4 dB, and when simulating errors in the communication channel 10 ^{-2, the} peak signal-to-noise ratio for the original and restored video is about 25.8 dB The resulting reconstructed video images are depicted in FIG.

An analysis of computational complexity showed that the complexity of the proposed encoding / decoding procedure is proportional to approximately m ² . Therefore, the proposed method for compressing and recovering messages can be implemented on modern signal processing processors.

Claims (2)

1. A method of compressing and restoring messages, which consists in the fact that previously on the transmitting and receiving sides they identically generate a random square matrix of size m × m elements, each element of which belongs to the range -500 ÷ +500, generate k random key matrices of size N × m and m × N elements, form a normalization matrix of size N × N elements, the elements of which C (i, j) are calculated by the formula

where i = 1, 2, ..., N, j = 1, 2, ..., N, form a matrix of quantized samples of a fixed grayscale video image of size M × M elements, in which each of its elements S (x, y) is assigned the quantized value of the corresponding pixel of a stationary grayscale video image, size M × M pixels, where x = 1, 2, ..., M; y = 1, 2, ..., M, form the matrix of coefficients of a two-dimensional discrete cosine transform of size M × M elements by sequentially multiplying the matrix of discrete cosine transform of size M × M elements by a matrix of quantized samples of a still grayscale video image of size M × M elements and on the transposed matrix of a discrete cosine transform of size M × M elements, form a matrix of coefficients of a two-dimensional discrete cosine transform of size N × N elements, according to the formula A (i, j) = L (i, j) , where L (i, j) -i, the jth element of the coefficient matrix of a two-dimensional discrete cosine transform of size M × M elements, A (i, j) -i, the jth element of the coefficient matrix of a two-dimensional discrete cosine transform of size N × N elements, moreover, select N × M, and then form a matrix of normalized values of size N × N elements by multiplying each coefficient matrix of the coefficients of a two-dimensional discrete cosine transform of size N × N elements A (i, j) by the corresponding element of the normalization matrix of size N × N elements, ge A random rectangular matrix of size N × m elements is generated, and a transposed random rectangular matrix of size N × m elements is taken as a random rectangular matrix of size m × N, then each of the key matrices of size N × m and m × N elements is added modulo 2 respectively, with a direct and transposed random rectangular matrix of sizes N × m and m × N elements, the resulting matrices are transformed by dividing the elements of each row of a random rectangular matrix of size N × m elements by the sum of units kits of the corresponding row and dividing the elements of each column of a random rectangular matrix of size m × N elements by the sum of the units of the corresponding column, k result matrices V (g) are calculated, where g = 1, 2, ..., k, size N × N elements, by sequentially multiplying k transformed random rectangular matrices of size N × m by a random square matrix of size m × m and by k converted random rectangular matrices of size m × N elements, each element of random rectangular matrices of size N × m and m × N elements, and after inversion transform them by dividing the elements of each row of a random rectangular matrix with an inverted element of size N × m elements by the sum of the units of the corresponding row and dividing the elements of each column of a random rectangular matrix with an inverted element of size m × N elements by the sum of the units of the corresponding column, recalculate k resulting matrices of size N × N elements by sequentially multiplying k transformed random rectangular matrices with inverted an element of size N × m onto a random square matrix of size m × m and to k transformed random rectangular matrices with an inverted element of size m × N, a random rectangular matrix of size N × m is transmitted via the communication channel, this matrix is received from the communication channel, then each of key matrices of sizes N × m and m × N elements are summed modulo 2, respectively, with direct and transposed random rectangular matrices of sizes N × m and m × N elements, transform the received random rectangular matrices of size N × m and m × N by doing k of the elements of the row of each random rectangular matrix of size N × m elements by the sum of the units of the corresponding row and the division of the elements of each column of the random rectangular matrix of size m × N elements by the sum of the units of the corresponding column, k restored result matrices are calculated

(g), where g = 1, 2, ..., k of size N × N elements, by sequentially multiplying k transformed random rectangular matrices of size N × m by a random square matrix of size m × m and by k transformed random rectangular matrices of size m × N, respectively, the matrix of reconstructed coefficients of size N × N elements is supplemented with zeros to the dimensions of M × M elements, a matrix of reconstructed coefficients of discrete cosine transforms of size M × M elements is obtained, the matrix of a fixed grayscale image is restored, p Then, by sequentially multiplying the transposed matrix of the discrete cosine transform with the size of M × M elements by the matrix of the reconstructed coefficients of the two-dimensional discrete cosine transform with the size of M × M elements and by the matrix of the discrete cosine transform by the size of M × M elements, a digital information signal is generated, each pixel of a fixed grayscale video images assign the value of the corresponding element of the matrix of reconstructed quantized fixed grayscale samples video images of size M × M elements, characterized in that after calculating k resulting matrices, calculate the total matrix size N × N elements V _s according to the formula

then the mean square error between the elements of the normalized value matrix of N × N elements and the elements of the total matrix V _s , the size of N × N elements is calculated, and after the inversion of each element of random rectangular matrices of sizes N × m and m × N, k resulting matrices are recalculated, the total matrix V _s and the mean square error between the matrix elements of the normalized values of size N × N elements and elements recalculated total matrix V _s size N × N elements, and the resulting mean square oshi Ku is subtracted from the previous mean square error in the case of a positive difference inverted stored element, after calculating the resultant reconstructed matrices k

(g) calculate the restored total matrix size N × N elements

_s by the formula

2. The method according to claim 1, characterized in that to obtain a matrix of restored coefficients of size N × N elements, the restored total matrix of size N × N elements is converted by elementwise division of its elements into corresponding elements of the normalization matrix of size N × N elements.

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