RU2645290C1 - Method of encoding digitized images using adaptive orthogonal conversion - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method for encoding a digital image is proposed. According to the method, the digital space of the digital image is converted, the image is divided into blocks with a size of the P×N elements, each block with a size of the P×N elements is adaptively encoded, a bitstream is formed. Herewith the adaptive coding is performed by defining a basis of the orthogonal conversion, and to determine the basis of the orthogonal conversion, the right-hand matrix of the orthogonal conversion with a size of N×N and the left-hand matrix of the orthogonal conversion with a size of the P×P elements are calculated.

EFFECT: increasing the compression ratio without reducing the quality of the restored image at the reception by eliminating the pre-formed wavelet-basis library and forming an orthogonal conversion basis directly from the original image block itself.

2 cl, 10 dwg, 1 tbl

Description

The claimed invention relates to the field of telecommunications and information technology, namely to the compression of digitized images.

The claimed invention can be used to reduce the requirements for image transmission speed and storage capacity used for storing images.

Currently existing video compression standards, for example MPEG-1, 2, 4, H-263, H-264, provide for the following typical conversion steps: encoding the color space of the image; separation of color components into blocks of a fixed size (4 × 4, 8 × 8, 16 × 16, 32 × 32, 64 × 64); execution of a two-dimensional discrete cosine transform (DKP-2) operation on each block; quantization of DCT-2 coefficients with subsequent entropy coding. The compression effect is achieved due to the fact that after performing DCT-2, most of the coefficients take a value close to zero. In this regard, the quantized blocks of coefficients contain a large number of zero elements, which provides a high compression ratio at the stage of entropy coding. The disadvantage of these standards is the need to separate the original image into smaller blocks. This leads to a significant drawback - the emergence of a blocking artifact, which manifests itself in the presence of visible boundaries between blocks of pixels in decoded images. This circumstance significantly worsens the visual perception of images with increasing compression ratio. The use of DCT-2 for image compression is described in detail in ISO / IEC 10918-1: 1993.

There is also known a method and apparatus for encoding and decoding an image, and a method and apparatus for decoding an image using the adaptive scanning order of coefficients according to RF patent 2518935 IPC H04N of 06/10/2014, which consists in the fact that on the transmitting side the original image is divided into smaller blocks, perform on the indicated blocks DKP-2, quantize them and perform entropy coding on the quantized coefficients, characterized by using the adaptive order of scanning the coefficients of DKP-2 by roetsirovaniya coefficients on the axis angle α (equal to 0, 45 or 90 degrees) to the reference axis and coded using an entropy coding on a predetermined scanned angle α and the coefficients.

The disadvantage of this analogue method is the limited number of scanning options for the coefficients, which is determined by a predetermined angle α, which leads either to a decrease in the compression ratio for a given quality of the restored images, or to a decrease in the quality of recovery with an increase in the compression ratio. In addition, since DCT-2 is performed on blocks of a smaller size than a compressible image, there remains a disadvantage associated with the blocking effect when restoring images on reception.

Another compression method is based on sub-band image conversion followed by elimination of inter-band redundancy. The subband transform is discussed in detail in the book of V.P. Vorobiev, V.G. Gribinin "Theory and practice of wavelet transform". - St. Petersburg, VUS, 1999. Using a sub-band transform, the image is converted into a set of sub-bands, each of which is a matrix of transform coefficients. As a subband transform, wavelet decomposition according to the Mall scheme is used. In this case, the implementation of the wavelet transform is used in the form of a mirror filter with a kernel, the form of which is determined by the used wavelet basis. Adaptation consists in choosing the low-frequency or high-frequency component of the mirror filter for each subband.

This analogue due to the adaptive choice of the frequency components of the subbands provides an increase in the compression ratio compared to methods in which the choice of the frequency components of the subbands is fixed.

The disadvantage of this analogue is that when the image is compressed, an unchanged wavelet basis is used, which does not allow for the required compression ratio when encoding the entire variety of different images.

The closest in technical essence to the claimed method of encoding digitized images is a method of encoding digitized images using a discrete wavelet transform adaptively defined basis according to patent RU 2429541 C2, IPC G06T 9/20 (2006/1) from 02.09.2009. The prototype method of encoding digitized images is that the original image is divided into blocks and for the said blocks a discrete wavelet transform is performed using wavelet bases that were determined adaptively at the stage of adaptive coding.

The prototype method of encoding digitized images reduces the requirements for image transmission speed and storage capacity by increasing the compression ratio by choosing the optimal wavelet basis from the library.

The general scheme of the prototype method is shown in FIG. 1. On the transmitting side, the input image 1 is subjected to color space conversion in step 2, the result of which is a matrix of pixels corresponding to the color spaces of the image (for example, a brightness matrix, a contrast matrix and a color matrix). Each of these matrices is passed to the image sampling stage 3, in which it is segmented and blocks of the original image are formed (hereinafter referred to as the BII). Then, step 4 of adaptive coding is performed using the methods of statistical, correlation and spectral analysis, for which the wavelet bases for the BII are adaptively determined, a discrete wavelet transform (hereinafter referred to as fiberboard) is performed, and also other actions for coding of the BII are performed. The method for determining the wavelet basis can be either one for all BIIs, or vary from block to block. In addition, when calculating the DVT coefficients of the BII subbands for each of these subbands, a wavelet basis can be used. At the final step 5, an image bitstream is formed. The obtained bit sequences for each of the BIIs are supplemented with overhead information (for example, information about block sizes, image sizes, used wavelet bases, etc.) and are combined into an image bitstream. The end of step 5 means the end of the compression of the input image 1, and the resulting bit sequence in step 6 can be recorded by the storage device or transmitted over the communication channel.

The prototype method provides several options for the adaptive determination of wavelet bases for BII: based on the calculation of the characteristics of the BII; based on the calculation of the characteristics of the BII subbands; based on the recovery estimate of the image blocks. Moreover, each of these options involves the selection of the optimal wavelet basis from the library of bases.

If it is necessary to restore the image, the recorded or transmitted bit sequence is decompressed. At decompression step 7, the image bitstream is analyzed, service information is extracted, and bit sequences corresponding to the encoded fiberboard coefficients for the BII are extracted. The obtained overhead information and bit sequences allow decoding in step 8 and the reverse fiberboard for the corresponding basic functions in step 9 in order to obtain blocks of the reconstructed image. The blocks of the reconstructed image obtained in step 9 are combined in accordance with the service information in step 10 into matrices of color spaces of the reconstructed image. After all the image matrices are restored, the stage of converting color spaces 11, which is a restored image in the form of matrices of the desired color space, begins. The decompression result is a reconstructed image 12.

A feature of the prototype method is that the choice of the optimal wavelet basis is carried out from the library of wavelet bases of a limited volume. Since the variety of compressible images is infinitely large, and the volume of the wavelet basis library is limited, there may be cases when the selected wavelet basis for compressing the current BII will not be optimal. This, in turn, leads either to a decrease in the quality of the images restored at the reception, or to a decrease in the compression ratio.

The disadvantage of the closest analogue (prototype) is a limited set of wavelet bases, from which the optimal one is selected, which leads to a decrease in compression efficiency (compression coefficient).

The purpose of the claimed technical solution is to develop a method for encoding a digital image that provides an increase in the compression ratio without reducing the quality of the image restored at the reception by eliminating the pre-formed library of wavelet bases and forming the basis of the orthogonal transformation directly from the BII itself.

корреляционных матриц X_i, i=1, 2, …,

по формулe

; k, n=1, 2, …, m_p, где X_i(k,n) - k-ый, n-ый элемент i-ой корреляционной матрицы; а(j,k+(i-1)m_p) - элемент блока исходного изображения размером P×N элементов, расположенный в j-ой строке и k+(i-1)m_p столбце; a(j,n+(i-1)m_p - элемент блока исходного изображения размером P×N элементов, расположенный в j-ой строке и n+(i-1)m_p столбце, затем, используя QR-алгоритм вычисления собственных векторов и собственных чисел квадратной симметрической матрицы, для каждой матрицы X_i, i=1, 2, …,

, вычисляют матрицу собственных векторов V_i и диагональную матрицу собственных чисел [diagλ]_i, i=1, 2, …,

, такие, что X_i=V_i[diagλ]_i, причем abs(λ_i(1,1))>abs(λ_i(2,2))>,…,>abs(λ_i(j,j))>,…,>abs(λ_i(m_p,m_p)), где λ_i(j,j) - j-ый, j-ый элемент i-ой диагональной матрицы собственных чисел [diagλ]_i, после чего присваивают элементам матрицы WP размером N×N элементов элементы матриц собственных векторов V_i, i=1, 2, …,

по формуле WP(k+(i-1)m_p, i+(j-1)m_p)=V_i(k,j), k=1, 2, …, m_p; i=1, 2, …,

; j=1, 2, …, m_p, а для вычисления левосторонней матрицы ортогонального преобразования предварительно назначают величину коэффициента m_l, кратную Р, причем m_l<<P, и формируют нулевую матрицу WL размером P×P элементов, затем вычисляют

корреляционных матриц Y_i, i=1, 2, …,

по формуле

; k, n=1, 2, …, m_l, где Y_i (k, n) - k-ый, n-ый элемент i-ой корреляционной матрицы; a(k+(i-1)m_l,j) - элемент блока исходного изображения размером P×N элементов, расположенный в k+(i-1)m_l строке и в j-ом столбце; а(n+(i-1)m_l,j) - элемент блока исходного изображения размером P×N элементов, расположенный в n+(i-1)m_l строке и в j-ой строке, затем, используя QR-алгоритм вычисления собственных векторов и собственных чисел квадратной симметрической матрицы, для каждой матрицы Y_i, i=1, 2, …,

, вычисляют матрицу собственных векторов U_i и диагональную матрицу собственных чисел [diagϒ]_i, i=1, 2, …,

, такие, что Y_i=U_i[diagϒ]_i, причем abs(ϒ_i(1,1))>abs(ϒ_i(2,2))>,…,>abs(ϒ_i(j,j))>,…,>abs(ϒ_i(m_p,m_p)), где ϒ_i(j,j) - j-ый, j-ый элемент i-ой диагональной матрицы собственных чисел [diagϒ]_i, после чего присваивают элементам матрицы WL размером P×P элементов элементы матриц собственных векторов U_i, i=1, 2, …,

по формуле WL(i+(j-1)m_l,k+(i-1)m_l)=U_i(k,j), k=1, 2, …, m_l; i=1, 2, …,

; j=1, 2, …, m_l, после этого выполняют двумерное ортогональное преобразование блока исходного изображения размером P×N элементов по формуле С=WL⋅A⋅WP, где С - матрица коэффициентов двумерного ортогонального преобразования размером P×N элементов; WL - левосторонняя матрица ортогонального преобразования размером P×P элементов; WP - правосторонняя матрица ортогонального преобразования размером N×N элементов; A - матрица блока исходного изображения размером P×N элементов.The specified technical result in the claimed method of encoding digitized images using adaptive orthogonal conversion is achieved by the fact that in the known encoding method, which consists in converting the digital space of a digital image, dividing the image into blocks of P × N elements, adaptive encoding of each block of P × N elements , the formation of the bit stream, according to the invention, adaptive coding is performed by determining the basis of the orthogonal transform and for the mentioned blocks, a two-dimensional orthogonal transformation is performed using the basis of the orthogonal transformation, which was determined adaptively at the stage of adaptive coding; in addition, the determination of the basis of the orthogonal transformation is performed by calculating the right-sided matrix of the orthogonal transformation of size N × N elements and the left-sided matrix of the orthogonal transformation of size P × P elements , and to calculate the right-hand matrix of the orthogonal transformation significant coefficient value m _p a multiple N, where m _p << N, and form a zero matrix WP size N × N elements, is then calculated

correlation matrices X _i , i = 1, 2, ...,

according to the formula

; k, n = 1, 2, ..., m _p , where X _i (k, n) is the k-th, n-th element of the i-th correlation matrix; and (j, k + (i-1) m _p ) is the element block of the original image with the size of P × N elements located in the j-th row and k + (i-1) m _p column; a (j, n + (i-1) m _p is the element block of the original image with the size of P × N elements located in the j-th row and n + (i-1) m _p column, then using the QR algorithm for calculating the eigenvectors and eigenvalues of a square symmetric matrix, for each matrix X _i , i = 1, 2, ...,

, calculate the matrix of eigenvectors V _i and the diagonal matrix of eigenvalues [diagλ] _i , i = 1, 2, ...,

such that X _i = V _i [diagλ] _i , and abs (λ _i (1,1))> abs (λ _i (2,2))>, ...,> abs (λ _i (j, j) )>, ...,> abs (λ _i (m _p , m _p )), where λ _i (j, j) is the jth, jth element of the ith diagonal eigenvalue matrix [diagλ] _i , after which assign elements of matrices WP of size N × N elements to elements of matrices of eigenvectors V _i , i = 1, 2, ...,

by the formula WP (k + (i-1) m _p , i + (j-1) m _p ) = V _i (k, j), k = 1, 2, ..., m _p ; i = 1, 2, ...,

; j = 1, 2, ..., m _p , and to calculate the left-sided matrix of the orthogonal transformation, the coefficient m _l is a multiple of P, m _l << P, and a zero matrix WL of size P × P elements is formed, and then the

correlation matrices Y _i , i = 1, 2, ...,

according to the formula

; k, n = 1, 2, ..., m _l , where Y _i (k, n) is the k-th, n-th element of the i-th correlation matrix; a (k + (i-1) m _l , j) is the element block of the original image with the size of P × N elements located in k + (i-1) m _l row and in the j-th column; and (n + (i-1) m _l , j) is the element block of the original image with the size of P × N elements located in the n + (i-1) m _l line and in the j-th line, then using the QR algorithm for calculating the eigenvalues vectors and eigenvalues of a square symmetric matrix, for each matrix Y _i , i = 1, 2, ...,

, calculate the matrix of eigenvectors U _i and the diagonal matrix of eigenvalues [diagϒ] _i , i = 1, 2, ...,

such that Y _i = U _i [diagϒ] _i , and abs (ϒ _i (1,1))> abs (ϒ _i (2,2))>, ...,> abs (ϒ _i (j, j) )>, ...,> abs (ϒ _i (m _p , m _p )), where ϒ _i (j, j) is the j-th, j-th element of the i-th diagonal eigenvalue matrix [diagϒ] _i , after which assign elements of the matrix WL of size P × P elements to the elements of the matrices of eigenvectors U _i , i = 1, 2, ...,

by the formula WL (i + (j-1) m _l , k + (i-1) m _l ) = U _i (k, j), k = 1, 2, ..., m _l ; i = 1, 2, ...,

; j = 1, 2, ..., m _l, then perform a two-dimensional orthogonal transform block size of the original image P × N elements of the formula C = WL⋅A⋅WP, where C - a two-dimensional matrix of coefficients of the orthogonal transformation size P × N elements; WL is the left-sided orthogonal transformation matrix with the size of P × P elements; WP is a right-handed orthogonal transformation matrix of size N × N elements; A is the matrix of the block of the original image with the size of P × N elements.

In the proposed method for encoding digitized images using adaptive orthogonal transform, the determination of the basis of the orthogonal transform is performed on the basis of the matrix of the block of the original image with the size of P × N elements, without the need for preliminary creation of the library of bases. Therefore, a new set of actions when performing encoding of digitized images using adaptive orthogonal transformation allows either to improve the quality of the images restored at the reception, or to increase their compression ratio due to adaptive calculation of the basis on the basis of the encoded image.

The claimed method is illustrated by drawings, which show:

FIG. 1 is a general diagram of compression and decompression in the closest analogue (prototype);

FIG. 2 - stages of adaptive coding of the claimed conversion method;

FIG. 3 - steps for calculating a right-handed orthogonal transformation matrix;

;FIG. 4 - assignment of elements of the matrix WP of sizes N × N elements of the matrices of eigenvectors V _i , i = 1, 2, ...

;

FIG. 5 - steps for calculating a left-handed orthogonal transformation matrix;

FIG. 6 - formation of the i-th correlation matrix of the left-sided matrix of the orthogonal transformation with the size of P × P elements;

FIG. 7 is an example of a source image of size 1080 × 1920 pixels;

FIG. 8 is a fragment of a reconstructed image using the JPEG algorithm;

FIG. 9 is a fragment of the reconstructed image using the JPEG-2000 algorithm;

FIG. 10 is a fragment of a reconstructed image using the inventive method.

The implementation of the inventive method consists in converting the digital space of a digital image, dividing the image into blocks of P × N elements, adaptively encoding each block in the size of P × N elements, generating a bit stream, and differs from the prototype method by performing the adaptive encoding stage during image compression. FIG. 2 illustrates adaptive coding steps of a transform method of the invention. In FIG. 2 BII 1, represented by a matrix A of size P × N elements, is used to calculate the basis of the orthogonal transformation in the form of a right-hand matrix of orthogonal transformation - WP of size N × N elements and a left-side matrix of orthogonal transformation - WL of size P × P elements. The matrices WP and WL are calculated in steps 2 and 3, respectively. After calculating the matrices WP and WL, in step 4, a two-dimensional orthogonal transformation is performed, as a result of which the coefficients of the two-dimensional orthogonal transformation are calculated in the form of a matrix C of size P × N elements in accordance with the expression C = WL⋅A⋅WP.

по формуле

(см. фиг. 6); k, n=1, 2, …, m_p. Затем, на этапе 3, для найденных матриц X_i, i=1, 2, …,

вычисляют матрицы собственных векторов V_i и диагональные матрицы собственных чисел [diagλ]_i, i=1, 2, …,

. Вычисление матриц собственных векторов и диагональных матриц собственных чисел можно осуществить так, как это показано в работе [Б. Парлет Симметричные проблемы собственных значений. Численные методы: Пер. с англ. - М, 1983. 384 с]. На 4 этапе присваивают элементам предварительно сформированной нулевой матрицы WP размером N×N элементов элементы матриц собственных векторов V_i, i=1, 2, …,

в соответствии с выражением WP(k+(i-1)m_p, i+(j-1)m_p)=V_i(k,j), k=1, 2, …, m_p; i=1, 2, …,

; j=1, 2, …, m_p. Присвоение элементам матрицы WP размеров N×N элементов матриц собственных векторов V_i, i=1, 2, …

показано на фиг. 4.The steps of computing the right-handed orthogonal transform matrix are shown in FIG. 3. The initial data for calculating the matrix WP of size N × N elements is BII 1 in the form of a matrix A of size P × N elements and the coefficient m _p , which determines the number of nonzero elements in each column of the matrix WP of size N × N elements. At stage 2, using the elements a (i, j), i = 1, 2, ..., P; j = 1, 2, ..., N, matrices A calculate the correlation matrices X _i , i = 1, 2, ...,

according to the formula

(see Fig. 6); k, n = 1, 2, ..., m _p . Then, in step 3, for the found matrices X _i , i = 1, 2, ...,

calculate the matrix of eigenvectors V _i and the diagonal matrix of eigenvalues [diagλ] _i , i = 1, 2, ...,

. The calculation of eigenvector matrices and diagonal eigenvalue matrices can be carried out as shown in [B. Parlet Symmetric eigenvalue problems. Numerical methods: Per. from English - M, 1983. 384 s]. At the 4th stage, the elements of the matrices of eigenvectors V _i , i = 1, 2, ..., are assigned to the elements of the preformed zero matrix WP of size N × N elements

in accordance with the expression WP (k + (i-1) m _p , i + (j-1) m _p ) = V _i (k, j), k = 1, 2, ..., m _p ; i = 1, 2, ...,

; j = 1, 2, ..., m _p . Assignment to the elements of the matrix WP of sizes N × N elements of the matrices of eigenvectors V _i , i = 1, 2, ...

shown in FIG. four.

по формуле

; k, n=1, 2, …, m_l. Затем, на этапе 3, для найденных матриц Y_i, i=1, 2, …,

вычисляют матрицы собственных векторов U_i и диагональные матрицы собственных чисел [diagϒ]_i, i=1, 2, …,

. На 4 этапе присваивают элементам предварительно сформированной нулевой матрицы WL размером Р×Р элементов элементы матриц собственных векторов U_i, i=1, 2, …,

в соответствии с выражением WL(i+(j-1)m_l, k+(i-1)m_l)=U_i(k,j), k=1, 2, …, m_l; k=1, 2, …,

; j=1, 2, …, m_l.The steps of computing the left-handed orthogonal transform matrix are shown in FIG. 5. The initial data for calculating the matrix WL of the size of P × P elements is BII 1 in the form of a matrix A of size P × N elements and the parameter m _l , which determines the number of nonzero elements in each row of the matrix WL of size P × P elements. At stage 2, using the elements a (i, j), i = 1, 2, ..., P; j = 1, 2, ..., N, matrices A calculate the correlation matrices Y _i , i = 1, 2, ...,

according to the formula

; k, n = 1, 2, ..., m _l . Then, in step 3, for the found matrices Y _i , i = 1, 2, ...,

calculate the matrix of eigenvectors U _i and the diagonal matrix of eigenvalues [diagϒ] _i , i = 1, 2, ...,

. At the 4th stage, the elements of the matrices of eigenvectors U _i , i = 1, 2, ..., are assigned to the elements of the preformed zero matrix WL of size P × P elements.

in accordance with the expression WL (i + (j-1) m _l , k + (i-1) m _l ) = U _i (k, j), k = 1, 2, ..., m _l ; k = 1, 2, ...,

; j = 1, 2, ..., m _l .

Verification of the effectiveness of the claimed method of encoding digitized images using adaptive orthogonal transformation was carried out by simulation.

A monochrome image with 256 gray levels of size 1080 × 1920 pixels was used as the initial one. An example of the original image is shown in FIG. 7. The results of simulation are presented in table 1.

, где P - число строк блока исходного изображения; N - число столбцов блока исходного изображения; A(i,j) - элемент блока исходного изображения размером P×N элементов, расположенный в i-ой строке и j-ом столбце;

- элемент блока восстановленного изображения размером P×N элементов, расположенный в i-ой строке и j-ом столбце. Представленные в табл. 1 значения PSNR получены при сжатии исходного изображения в 100 раз. Кроме заявленного способа в таблице 1 представлены результаты вычисления PSNR при использовании известных стандартов сжатия неподвижных изображений JPEG и JPEG-2000. Анализ результатов показывает, что заявленный способ характеризуется превышением величины PSNR на 5,1 [дБ] по сравнению с алгоритмом JPEG и на 2,5 [дБ] по сравнению с алгоритмом JPEG-2000.During the simulation, the quality of the reconstructed images was evaluated by calculating the peak signal-to-noise ratio (PSNR) and visual viewing. The calculation of PSNR was carried out in accordance with the expression

where P is the number of lines of the block of the source image; N is the number of columns of the block of the source image; A (i, j) - element block of the original image with the size of P × N elements located in the i-th row and j-th column;

- an element of a reconstructed image block of size P × N elements located in the i-th row and j-th column. Presented in the table. 1, PSNR values are obtained by compressing the original image 100 times. In addition to the claimed method, table 1 presents the results of the calculation of PSNR using well-known compression standards for still images JPEG and JPEG-2000. Analysis of the results shows that the claimed method is characterized by the excess of the PSNR by 5.1 [dB] compared to the JPEG algorithm and by 2.5 [dB] compared to the JPEG-2000 algorithm.

A visual analysis of the quality of the reconstructed images showed that the images obtained on the basis of the claimed method do not have block artifacts (see Fig. 8) characteristic of the JPEG algorithm and artifacts in the form of highlighting background areas characteristic of the JPEG-2000 algorithm ( see Fig. 9). A fragment of the reconstructed image based on the claimed method is shown in FIG. 10. Analysis of the presented image indicates the absence of these artifacts.

Thus, in the claimed method of encoding digitized images using adaptive orthogonal conversion, the quality of the reconstructed images is improved at a given compression ratio compared to the known ones.

Claims (2)

1. A method of encoding a digital image, which consists in converting the digital space of a digital image, dividing the image into blocks of P × N elements, adaptively encoding each block of P × N elements, forming a bit stream, characterized in that adaptive encoding is performed by determining the basis of the orthogonal transformation, and to determine the basis of the orthogonal transformation, calculate the right-sided matrix of the orthogonal transformation of size N × N and the left-sided matrix of ortho of a global transformation of size P × P elements and then, for said blocks of size P × N elements, a two-dimensional orthogonal transformation is performed using the previously determined basis of the orthogonal transformation, and a coefficient m _p multiple of N is preliminarily assigned to calculate the right-hand matrix of the orthogonal transformation, and m _p <<N, and form a zero matrix WP of size N × N elements, then calculate

correlation matrices X _i ,

according to the formula

k, n = 1, 2, ... m _p , where X _i (k, n) is the k-th, n-th element of the i-th correlation matrix; a (j, k + (i-1) m _p ) is the element block of the original image located in the j-th row and in the k + (i-1) m _p column; a (j, n + (i-1) m _p is the image element located in the j-th row and in the n + (i-1) m _p column, then using the QR algorithm for calculating the eigenvectors and eigenvalues of the square symmetric matrix for of each correlation matrix X _i ,

calculate the matrix of eigenvectors V _i and the diagonal matrix of eigenvalues [diagλ] _i ,

such that X _i = V _i [diagλ] _i , and (abs (λ _i (1,1))> abs (λ ₁ (2,2))>, ...,> abs (λ _i (j, j ))>, ...,> abs (λ _i (m _p , m _p )), where λ _i (j, j) is the j-th, j-th element of the i-th diagonal eigenvalue matrix [diagλ] _i , after what is assigned to the elements of the matrix WP of size N × N elements the elements of the matrices of eigenvectors Vi,

in accordance with the expression WP (k + (i + 1) m _p , i + (j-1) m _p ) = V _i (k, j), k = 1, 2, ..., m _p ;

, j = 1, 2, ..., m _p , and to calculate the left-sided matrix of the orthogonal transformation, the coefficient value is preliminarily assigned

multiple of P, and

, and form a zero matrix WL of size P × P elements, then calculate

correlation matrices Y _i ,

according to the formula

k

where Y _i (k, n) is the k-th, n-th element of the i-th correlation matrix;

- an element block of the original image located in

row and in the jth column;

- an element block of the original image located in

row and in the jth column, then using the QR algorithm for calculating the eigenvectors and eigenvalues of the square symmetric matrix for each matrix Y _i ,

calculate the matrix of eigenvectors U _i and the diagonal matrix of eigenvalues

such that

moreover

Where

- j-th, j-th element of the i-th diagonal matrix of eigenvalues

then assign the elements of the matrix WL of size P × P elements the elements of the matrices of eigenvectors U _i ,

according to the expression

,

2. The method according to p. 1, characterized in that the two-dimensional orthogonal transformation of the block of the original image with the size of P × N elements is performed in accordance with the expression C = WL⋅A⋅WP, where C is the coefficient matrix of the two-dimensional orthogonal transformation with the size of P × N elements; WL is the left-sided orthogonal transformation matrix of size P × P elements; WP is a right-handed orthogonal transformation matrix of size N × N elements; A is the matrix block of the original image with the size of P × N elements.

Images