RU2419246C1 - Method to compress and recover fixed halftone video images - Google Patents

Abstract

FIELD: information technologies. ^ SUBSTANCE: matrix of frequency coefficients of a video image is calculated at the transmitting side by doing an operation of two-dimensional cosine conversion. Then 2p coefficients of two-dimensional linear forecasting (TDLFC) are calculated in a matrix of quantised counts of a fixed halftone image and are sent into a digital communication channel. The TDLFC quantised values are used to form an envelope of frequency coefficients, which is applied to determine coordinates of frequency coefficients in the order of their absolute values decreasing. Then values of frequency coefficients corresponding to the found coordinates are quantised and sent to the communication channel. When recovering messages on the basis of TDLFC received from the communication channels, an envelope of frequency coefficients is formed, using which, coordinates are assigned to the received frequency coefficients in the structure of their matrix, and the video image is recovered by doing an operation of a reverse two-dimensional discrete cosine conversion above the recovered matrix of frequency coefficients. ^ EFFECT: provision of compression and recovery of fixed halftone images with reduction of information transfer speed with preservation of the specified recovery quality. ^ 4 cl, 14 dwg, 1 app

Description

The invention relates to the field of telecommunications, and in particular to methods for transmitting video images through digital communication channels, mainly low speed.

Known methods of encoding video images based on statistical coding and prediction coding, see, for example, the book: W. Prett. Digital image processing. Part 2. - M .: Mir, 1982, p.641-688. In these methods, bitwise processed images are encoded 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 in the processing of digital signals. - M.: Radio and communications, 1980, p.192-201; M. Leonard, A Scheme Implementing an Algorithm for Compressing Images of Fixed Objects // Electronics, 1991. No. 10, P.20-24), including three operations: first, the image undergoes two-dimensional orthogonal transformation, the resulting conversion coefficients are quantized, and subsequently encoded for transmission over communication channel.

The disadvantage of the above analogue methods is the relatively high speed of message transmission for a given quality of their recovery at the reception.

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. 2226043, IPC ⁷ H04N 7/30 from 03/20/04

The known prototype method is that previously randomly on the transmitting side and on the receiving side generate a random square matrix of size m × m elements. Random rectangular matrices are generated from single and zero elements of size N × m and m × N elements, random rectangular matrices of size N × m and m × N elements 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 the units of the corresponding column. A matrix of N × N elements is calculated by successively multiplying the resulting rectangular matrix of N × m elements after transformation, a random square matrix of m × m elements and obtained after the transformation of a rectangular matrix of m × N elements. Each element of random rectangular matrices of size N × m and m × N elements is sequentially inverted. Then, random rectangular matrices of N × m and m × N elements are recalculated and the matrix of N × N elements is recalculated by successively multiplying the resulting rectangular matrix of N × m elements, a random square matrix of m × m elements and obtained after the transformation rectangular matrix of size m × N elements. Subtract the sum of the squares of the difference from the same amount obtained in the previous step, and, in the case of a positive difference, save the inverted value of the element, and otherwise, perform its repeated inversion. The set of zero and single elements of rectangular matrices of size N × m and m × N elements is transmitted over the communication channel, the set of zero and single elements of rectangular matrices of size N × m and m × N elements is transmitted from the communication channel and they are converted by dividing the elements of each row of the rectangular matrices of size N × m elements by the sum of units of the corresponding row and dividing the elements of each column of a rectangular matrix of size m × N elements by the sum of units of the corresponding column. Each element of a random square matrix of size m × m elements belongs to the range -500 ÷ + 500. As a message to be compressed and restored, a stationary grayscale video image is used, from which a matrix of quantized samples of a stationary grayscale video image of size M × M elements is formed, assigning each of its elements S (x, y), where x = 1,2, ..., M ; y = 1,2, ..., M, the quantized value of the corresponding pixel of the still grayscale video image. The matrix of quantized samples of a fixed halftone video image of size M × M elements is converted to digital form, while the matrix of coefficients of a two-dimensional discrete cosine transform (DDC) of size M × M elements is preformed by multiplying the matrix of discrete cosine transform (DCT) of size M × M elements by a matrix quantized samples of a fixed grayscale video image of M × M size elements and the transposed matrix of discrete cosine transform times erom M × M elements. Form the matrix of coefficients of the DCTD with the size of N × N elements based on the expression A (i, j) = L (i, j), where i = 1,2, ..., N, j = 1,2, ..., N, L (i , j) is the i-th, j-th element of the matrix of coefficients of the DCTD size M × M elements, A (i, j) is the i-th, j-th element of the matrix of coefficients of the DCTD size N × N elements, and N≤M . On the transmitting and receiving sides, a normalization matrix of the size N × N elements is identical formed, the elements of which C (i, j) are calculated by the formula

.

.

Then, a matrix of normalized coefficients of the DCTD with the size of N × N elements is formed by multiplying each coefficient A (i, j) by the corresponding element of the normalization matrix with the size of N × N elements. After calculating a matrix of N × N elements, the sum of the squares of the differences between the elements of the matrix of N × N elements and the corresponding elements of the matrix of normalized DCT coefficients of N × N elements is calculated, and after recalculating the matrix of N × N elements, the sum of the squares of the differences between matrix elements of size N × N elements; and elements of a matrix of normalized coefficients of DCTD of size N × N elements. After the conversion, on the receiving side of the rectangular matrices of N × m and m × N elements in size, a matrix of restored normalized DCT coefficients of N × N elements is formed by sequentially multiplying the resulting rectangular matrix of N × m size, a random square matrix of m × m elements in size and obtained after transforming a rectangular matrix of size m × N elements. Then, a matrix of reconstructed DCT coefficients of N × N element size is formed by dividing the value of each i-th, j-th element of the matrix of restored normalized DCT coefficients of N × N elements by the corresponding element of the normalization matrix of N × N elements. A matrix of reconstructed DDKD coefficients with the size of M × M elements is formed by assigning the value of each i-th, j-th element of the matrix of reconstructed DDKP coefficients with the size of N × N elements to each i-th, j-th element of the matrix of restored DDKP coefficients with the size of M × M elements , and as the remaining elements, zeros are written. A matrix of reconstructed quantized samples of a fixed grayscale video image is formed by multiplying the transposed DCT matrix of M × M elements by a matrix of restored DCT coefficients of M × M elements and by a DCT matrix of M × M elements. A matrix of reconstructed quantized samples of a still halftone video image of size M × M elements is presented in the form of a motionless grayscale video image, assigning to each pixel of a motionless grayscale video image the value of the corresponding element of the matrix of reconstructed quantized samples of a still grayscale video image of size M × M elements.

When using the prototype method without compromising the quality of message recovery, the compression of the original images to a value at which it is possible to transmit stationary grayscale images through digital communication channels at a speed of 256 ÷ 512 kbit / s is possible.

The disadvantage of this prototype method is the relatively low quality of the reconstructed video images when using communication channels with limited bandwidth. This is because in the prototype method, the matrix of reconstructed quantized samples of a fixed halftone video image of size M × M elements is calculated by performing an inverse two-dimensional discrete cosine transform on a matrix of reconstructed coefficients of a discrete cosine transform of size M × M elements. Moreover, N × N elements of this matrix (N≤M) occupying its upper left quadrant are formed on the basis of a digital stream received from the communication channel, and the remaining elements are considered equal to zero.

In this case, an assumption is made that the N × N elements of the matrix of the DDKP contain the most significant (maximum in absolute value) coefficients. Such a construction of the decoder leads to the fact that in order to increase the compression coefficient, it is necessary to reduce the parameter N, which leads to an increase in the number of zero coefficients of the DCT matrix. On the other hand, a decrease in the value of N leads to the fact that significant coefficients of the DCT are also equated to a zero value. This, in turn, leads to a decrease in the quality of the restored images. Thus, the fixed configuration of nonzero DDCD coefficients in the form of an upper left quadrant of size N × N elements leads either to a low compression ratio with good quality of the reconstructed images, or to their low quality with a relatively high compression ratio.

The aim of the invention is to develop a method of compression and recovery of messages, providing improved quality of the recovered video images using low-speed communication channels.

This goal is achieved by the fact that in the known method of compressing and restoring messages, namely, that a stationary video image is converted to digital form, for which a matrix of quantized samples of a stationary video image is formed, its frequency coefficients (image spectrum matrix) are calculated by performing a two-dimensional discrete cosine operation transformations, quantize frequency coefficients whose values exceed a predetermined level and transmit them over the communication channel, according to the adopted frequency coefficient itsientam restore the matrix of quantized samples of the still image. In the presented method, after the formation of a matrix of quantized samples from the values of its elements, two-dimensional linear prediction coefficients ax ₁ , ax ₂ , ..., ax _p and ay ₁ , ay ₂ , ..., ay _p are calculated, where p is the prediction depth. Then they are quantized and transmitted to the communication channel, the envelope of the frequency coefficients is formed from the values of the quantized coefficients of the two-dimensional linear prediction. Using the generated envelope, the coordinates of the frequency coefficients are determined in descending order of their absolute values, then the values of the frequency coefficients corresponding to the found coordinates are quantized and sequentially transmitted to the communication channel, and the number K _{ots of} coefficients to be transmitted is pre-set depending on the required image restoration quality. After receiving two-dimensional linear prediction coefficients and frequency coefficients, the two-dimensional linear prediction coefficients form an envelope of frequency coefficients on the receiving side, as well as on the transmitting side, on which coordinates are assigned to the received frequency coefficients in the structure of the image spectrum matrix, and instead of the missing frequency coefficients in the structure matrices leave zero values. Then restore the image by multiplying the transposed matrix of the discrete cosine transform on the matrix of the restored coefficients of the two-dimensional discrete cosine transform and the matrix of the discrete cosine transform. A matrix of reconstructed quantized samples of a still grayscale video image is presented in the form of a grayscale video image by assigning each pixel of a grayscale video image the value of the corresponding element of the matrix of reconstructed quantized grayscale samples of a stationary grayscale video image.

Thanks to a new set of essential features, by calculating the envelope of the frequency coefficients of a fixed grayscale image and calculating the two-dimensional linear prediction coefficients of the spectrum matrix of this image, a significant reduction in the volume of the digital stream at the encoder output is provided. To reduce the digital representation of the video image, not all spectral coefficients are encoded and transmitted, but only K _{ots of} spectral coefficients from the spectral region with maximum energy.

Thus, the difference between the proposed compression method and the prototype method is that the region of significant spectrum coefficients is not fixed, but is determined for each compressible message by calculating the spectrum envelope based on two-dimensional linear prediction coefficients.

This allows you to improve the quality of the restored video when using communication channels with limited bandwidth.

The claimed method is illustrated by drawings:

- Figure 1 - Formation of a matrix of quantized samples;

- Figure 2 - Spectral representation of the conversion coefficients;

- Figure 3 - Representation of the i-th, j-th element of the brightness value of the i-th, j-th pixel of the original image as a linear combination of previous samples;

- Figure 4 - Formation of matrices Dy;

- Figure 5 - Formation of matrices Dx and M (j);

;- 6 - Calculation of the envelope on the lines ACHx (i),

;

;- Fig.7 - Calculation of the envelope on the columns ACHy (j),

;

- Fig - Calculation of the envelope of the coefficients of the DDKP;

- Fig.9 - The ranking of the matrix elements of the envelope of the coefficients of the DDKP in descending order of values;

- Figure 10 - Formation of a sequence of frequency coefficients to be transmitted over the communication channel;

- 11 - Recovery matrix DKKP on the receiving side;

- Fig - Compression and restoration of the 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 a message over a communication channel, for the transmission of which, under the conditions of limiting the speed of the provided communication channel, an unacceptably large time interval is required, various methods of reducing the digital representation of the transmitted message are used.

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. In this case, it is sufficient to transmit only the decomposition coefficients on the communication channel under the assumption that at the receiving side, similar (as in transmission) reference vectors will be used for message recovery.

Such a technique causes a certain decrease in the amount of information required for transmission over the communication channel, and at the same time achieve the required quality of the restored messages.

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. The proposed method solves the problem of reducing the amount of information transmitted while maintaining the required quality.

The proposed method includes the following steps.

As a message to be compressed and restored, a stationary halftone video image is considered (see Fig. 1a), from which a matrix of quantized samples of a stationary halftone video image of size P × N elements is formed, assigning each of its elements A (i, j), where i = 1,2, ..., P; j = 1,2, ..., N, the quantized value of the corresponding pixel of a stationary grayscale video image (see fig.1b and Fig.12 (1)).

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.

где

- матрица коэффициентов ДДКП размером P×N элементов,

- матрица квантованных отсчетов неподвижного полутонового видеоизображения размером P×N элементов,

- матрица прямого ДКП, размером Р×Р элементов;

- матрица обратного ДКП, размером N×N элементов (см. фиг.12 (2)).The matrix of coefficients of the DCTD with the size of PxN elements is formed based on the expression

Where

- the matrix of coefficients DKPP size P × N elements,

- a matrix of quantized samples of a stationary grayscale video image of size P × N elements,

- matrix direct DCT, size R × P elements;

- matrix inverse DCT, size N × N elements (see Fig. 12 (2)).

The most informative, in terms of the quality of restoration of the transmitted video image (see Fig. 2a), are the maximum-energy DCT coefficients, located, as a rule, in the upper left quadrant of the DCTD coefficient matrix with the size of P × N elements. However, studies show that the location of significant coefficients for different images may be different (see figb).

To determine the location of significant coefficients, find the envelope of the coefficients of the DCT. For this purpose, two-dimensional linear prediction coefficients ax ₁ , ax ₂ , ..., ax _p and ay ₁ , ay ₂ , ..., ay _p ,, are calculated, where p is the prediction depth (see Fig. 12 (3)). The value of p is chosen in the range from 8 to 12. This range of the choice of the number of calculated linear prediction coefficients is due to the fact that when p is less than 8, it is not possible to approximate the envelope of the video image spectrum with the necessary accuracy, while increasing the value of the parameter p more than 12 does not give any Any significant increase in approximation accuracy. To calculate the coefficients of two-dimensional linear prediction, as in the case of calculating the coefficients of one-dimensional linear prediction, it is necessary to solve the problem of minimizing the mean square error between the original and the predicted messages regarding these coefficients (see, for example, the books: J.D. Markel, A.Kh. Gray, Linear Prediction of Speech. - Moscow: Communication, 1980, pp. 13-23; A.A. Ustinov, A.A. Roshchin, D.A. Bardyukov. Parametric coding of speech with linear prediction. - St. Petersburg: YOU. , 2008, p.30-32).

Let us explain the features of calculating the coefficients of two-dimensional linear prediction.

Let A (i, j) be the i-th, j-th element of the brightness value of the i-th, j-th pixel of the original image, then the predicted value of the i-th, j-th image element

можно определить как линейную комбинацию p предшествующих элементов i-й строки и p предшествующих элементов j-го столбца (см. фиг.3):

can be defined as a linear combination of p previous elements of the i-th row and p previous elements of the j-th column (see figure 3):

,

.

,

.

For all elements of the jth column of the source image, this expression can be written in matrix form in the form:

,

,

where Dy (j) is a matrix of size P × p composed of elements of the jth column of the image (see Fig. 4a), having the form (see Fig. 4c):

имеющих вид (см. фиг.5б, в, г):M (j) is a matrix of size P × p elements (see Fig.5d), consisting of jx rows of matrices Dx (k),

having the form (see figb, c, d):

Based on the expression found for the jth predicted column, the problem of searching for prediction coefficients in the form of vectors ax and ay can be written in the form:

The solution to this problem is given in the appendix. After calculating the two-dimensional linear prediction coefficients, ax and ay convert them to a suitable form for quantization, quantize them and transmit to the communication channel, using the values of the quantized two-dimensional linear prediction coefficients, calculate the two-dimensional envelope of the DCT coefficients.

As noted above, prediction coefficients themselves are not quantized. This is explained by their high sensitivity to the influence of errors in the digital communication channel and the lack of clear ranges of dynamic change, which, in turn, complicates the process of quantization. Therefore, before quantization, an intermediate stage was introduced, which consists in converting prediction coefficients into a set of linear spectral frequencies (LSP) (see, for example, the book: A. A. Ustinov, A. A. Roshchin, D. A. Bardyukov. Parametric coding of speech with linear prediction. - SPb .: VAS, 2008, p. 37 -43).

To calculate the two-dimensional envelope of the coefficients of the DKDP determine the elements (see Fig.6 and 7, respectively):

,

,

,

,

,

, ax и ау - значения вычисленных 2p коэффициентов двумерного линейного предсказания. На основе найденных элементов ACH_x(i),

и ACH_y(j),

вычисляют элементы двумерной огибающей коэффициентов ДДКП в соответствии с выражением (см. фиг.8 и фиг.12(4)):where P and N are the dimensions of the image matrix,

,

, ax and ay are the values of the calculated 2p coefficients of two-dimensional linear prediction. Based on the found elements ACH _x (i),

and ACH _y (j),

calculate the elements of the two-dimensional envelope of the coefficients of the DCT in accordance with the expression (see Fig. 8 and Fig. 12 (4)):

The elements of the envelope matrix of the frequency coefficients are ranked (see Fig. 9a) in descending order of their values (see Fig. 9b). The envelope formed (see Fig. 8) determines the coordinates of the frequency coefficients in descending order of their absolute values. Then, the values of the frequency coefficients corresponding to the found coordinates are quantized and sequentially transmitted to the communication channel, and the number K _{ots of} coefficients to be transmitted is predetermined depending on the required image restoration quality (see Fig. 10 and Fig. 12 (5)).

After receiving two-dimensional linear prediction coefficients and frequency coefficients (see Fig. 12 (7)), the two-dimensional linear prediction coefficients form an envelope of frequency coefficients on the receiving side (see Fig. 12 (8)), as well as on the transmitting side ( see Fig. 8). According to the generated envelope (see Fig. 11a), the received frequency coefficients (see Fig. 11b) are assigned coordinates in the structure of the image spectrum matrix, and instead of the missing frequency coefficients in the matrix structure, zero values are left (see Fig. 11c and Fig. 12 ( 10)).

Next, a matrix of reconstructed quantized samples of a fixed grayscale video image is formed (see Fig. 12 (11)) by multiplying the transposed DCT matrix with a size of P × P elements by a matrix of restored DCT coefficients with a size of P × N elements and a DCT matrix of N × N elements, t .e. based on the formula:

,

,

- матрица восстановленных квантованных отсчетов неподвижного полутонового видеоизображения размером P×N элементов.Where

- a matrix of reconstructed quantized samples of a stationary grayscale video image with a size of P × N elements.

в виде неподвижного полутонового видеоизображения, присвоив каждому пикселю 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 each pixel of a motionless grayscale video image the value of the corresponding matrix element

.

In general, the process of compression and restoration of a stationary grayscale video image can be represented in the form of a circuit (see Fig. 12).

1 - matrix of quantized samples of a stationary grayscale video image;

2 - matrix of frequency coefficients of a fixed grayscale video image;

3 - coefficients of two-dimensional linear prediction of a matrix of a stationary grayscale video image 1;

4 - envelope of the frequency coefficients of a stationary grayscale video image;

5 is a sequence of frequency coefficients of a fixed grayscale video image to be transmitted;

6 - digital communication channel;

7 - reconstructed two-dimensional linear prediction coefficients of a matrix of a fixed grayscale video image 1;

8 - envelope of the frequency coefficients of a fixed grayscale video image, formed on the basis of 7;

9 is a sequence of received frequency coefficients of a fixed grayscale video image;

10 - reconstructed matrix of frequency coefficients of a fixed grayscale video image;

11 is a reconstructed matrix of quantized samples of a still grayscale video image.

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. In the proposed method, a high compression ratio 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 2p two-dimensional linear prediction coefficients and K _{ots of} the DCT coefficients.

Practical studies show that while leaving 1/16 of the spectral coefficients of the two-dimensional discrete cosine transform of the total number of coefficients of the matrix of two-dimensional discrete cosine transform coefficients of 512 × 512 elements, the peak signal-to-noise ratio for the original and reconstructed video image is about 40 dB.

With P and N equal to 512, the compression ratio at 40 dB corresponds to 50 times. Studies show that when compressing the original image in accordance with the prototype method, when compressing 50 times, the peak signal-to-noise ratio for the reconstructed image corresponds to 31 dB.

application

The task of searching for linear prediction coefficients ax and ay reduces to solving expression (1):

where Dy (j) is a matrix of size P × p, composed of elements of the j-th column of the image, having the form (see figure 5):

, имеющей вид (см. фиг.6):M (j) is a matrix of size P × p elements, consisting of j-rows of matrices Dx (k),

having the form (see Fig.6):

To calculate ax, we find the derivative of the objective function (1) with respect to the given vector and equate it to zero:

The vector of linear prediction coefficients ax is determined by solving equation (2):

To reduce the cumbersomeness of further calculations, we introduce the following notation:

We rewrite expression (3) with the newly introduced notation:

To find ay, we substitute expression (4) into the expression of the objective function:

Where

We find the derivative of the objective function (5) with respect to ay and equate it to zero:

Solving equation (6) with respect to ay, we obtain:

Thus, the sequential solution of equations (6) and (2) results in linear prediction coefficients ay and ax.

Claims (4)

1. The method of compression and recovery of stationary grayscale video images, which consists in the fact that the stationary video image is converted into digital form, for which a matrix of quantized samples of the stationary video image is formed, its frequency coefficients (image spectrum matrix) are calculated by performing the two-dimensional discrete cosine transform operation, frequency frequencies are quantized coefficients whose values exceed a predetermined level and transmit them over the communication channel, according to the accepted frequency coefficients of the recovery pour in a matrix of quantized samples of a still image, characterized in that after the formation of a matrix of quantized samples from the values of its elements, 2p coefficients of two-dimensional linear prediction ax ₁ , ax ₂ , ..., ax _p and ay ₁ , ay ₂ , ..., ay _p , where p - the depth of the prediction, then they are quantized and transmitted to the communication channel, according to the values of the quantized coefficients of the two-dimensional linear prediction, the envelope of the frequency coefficients is formed, which determine the coordinates of the frequency coefficients in descending order of their absolute values of the then values of frequency coefficients corresponding to the found coordinates are quantized and are sequentially transmitted to the communication channel, wherein the number K _ots be transmitted coefficients set previously, depending on the desired quality of image reconstruction, after receiving the coefficients of the two-dimensional linear prediction and frequency coefficients, the coefficients two-dimensional linear prediction form on the receiving side the envelope of the frequency coefficients, which assign to the adopted frequency coefficient cients coordinates in the matrix structure of the spectrum of the image, after which the reduced image by performing two-dimensional inverse discrete cosine transform on the reconstructed image array spectrum, instead of missing frequency coefficients in the matrix structure is left to zero. 2. The method according to claim 1, characterized in that the two-dimensional linear prediction coefficients are calculated by solving the problem of minimizing the mean square error between the matrices of the original and the predicted image, relative to the two-dimensional linear prediction coefficients ax ₁ , ax ₂ , ..., ax _p and ay ₁ , ay ₂ , ... ay _r , and their number p is chosen in the interval p = 8 ÷ 12. 3. The method according to claim 1, characterized in that the envelope of the frequency coefficients is formed by sequentially calculating the envelope according to the rows ACH _x (i) and columns ACH _y (j) of the matrix of frequency coefficients according to the formulas:

,

,
where P and N are the sizes of the image matrix, i = 1, N, j = 1, P, ax and ay are the values of the calculated 2p coefficients of two-dimensional linear prediction, and the full envelope of the frequency coefficients is calculated as the vector product:

. 4. The method according to claim 1, characterized in that the value of K _{ots is} chosen in accordance with the required quality of the restored image.

Images