RU2500067C2 - Image compression method - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: image compression method, based on excluding a certain portion of information, wherein the information is excluded from the space domain through numerical solution of Poisson or Laplace differential equations, and subsequent estimation of the difference between the obtained solution and actual values at discrete points of the image; generating an array of boundary conditions, which includes a considerable number of equal elements which is compressed, and the image is reconstructed by solving Poisson or Laplace partial differential equations using the array of boundary conditions.

EFFECT: eliminating loss of image integrity, high efficiency of compressing images having large areas of the same tone or gradient and maintaining contrast of boundaries between different objects of an image.

2 cl, 16 dwg

Description

The invention relates to the field of digital signal processing and can be used for compression (compression) of static and dynamic images, that is, data conversion in order to reduce its volume, both without loss and with the loss of part of the information.

In the modern world, an avalanche-like growth of media content is observed, therefore data compression is an actual area of scientific research.

Known methods of lossless data compression based on the use of statistical information (repetition, autocorrelation) and lossy compression based on the removal of redundant (not significant or non-critical) information (Watolin D., Ratushnyak A., Smirnov M., Yukin V Methods of data compression. M: Dialog - MEPhI, 2003; Salomon D. Compression of data, images and sound. M.: TECHNOSPHERE, 2004). These methods are applied both individually and in various combinations. Lossless compression is applied to two-level (single-bit), multi-level and full-color images. The most common implementations of lossless bitmap compression algorithms are GIF (S.Blackstock. LZW and GIF explained. Http://www.martinreddy.net/gfx/2d/GIF-comp.txt) (static and dynamic images) and PNG (PNG home page. http://www.libpng.org/pub/png/png.html). These methods are based on vocabulary encodings based on modifications of the Huffman transform and LZ77, LZ78 (LZW - Lempel, Ziv, Welch).

A fractal image compression method is known, based on the fact that an image can be represented more compactly using coefficients of a system of iterable functions (D. Saupe, R. Hamzaoui, H. Hartenstein. Fractal image compression - An introductory overview, in: Fractal Models for Image Synthesis , Compression, and Analysis, D. Saupe, J. Hart (eds.), ACM SIGGRAPH'96 Course Notes).

Known methods are those in which the images using the brush fire method (forest fire) form a polygon skeleton 1-2 pixels thick, which is a Voronoi diagram. The difficulties in the practical implementation of such methods include: the formation of the correct skeleton in the form of a connected graph (Skien S. Algorithms. Development Guide. - 2nd ed. Transl. From English. - SPb .: BHV-Petersburg, 2011).

A known interpolation method for compressing a television signal (RF patent No. 2111172, priority date 10/12/1996, IPC H04N 5/335, published 05/27/1999), which is based on the artificial exclusion of fragments of signal lines and their recovery using interpolation by fragments not excluded parts of lines, which will reduce the redundancy of the television signal.

There is a method of lossy compression based on discrete cosine transform (DCT), designed for static and dynamic images, which is the closest in combination of essential features to the claimed method and adopted as a prototype (Stephen Smith. Digital signal processing. A practical guide for engineers and scientific workers.Translated from English by Linovich A.Yu., Vityazev S.V., Gusinsky I.S. - M .: Dodeka-XXI, 2011, p. 548). In this method, the common JPEG format uses the discrete cosine transform (DCT) for compression, followed by a modified Huffman transform. The basis of JPEG compression is to obtain the spatial spectrum of the image, followed by the exclusion of some of the spectral components, which subsequently allows you to restore the image in sufficient quality. The resulting image spectrum, due to the fact that it can contain a significant number of repeating individual elements and chains, is effectively compressed.

In JPEG compression, the spatial spectrum is obtained by two-dimensional DCT of the image matrix U of size M × N in accordance with the expression:

$$B{}_{pq}={\alpha }_p{\alpha }_q{\displaystyle \sum _{m=0}^{M-\mathrm{one}}{\displaystyle \sum _{n=0}^{N-\mathrm{one}}{A}_{mn}\cos \frac{\pi (2m+\mathrm{one})p}{2M}\cos \frac{\pi (2n+\mathrm{one})q}{2N},(\mathrm{one})}}$$

where 0≤p≤M-1, 0≤q≤N-1;

$${\alpha }_p=\{\begin{array}{c}\frac{\mathrm{one}}{\sqrt{M}},e\mathrm{from}l\mathrm{and}p=0;\\ \sqrt{\frac{2}{M}},e\mathrm{from}l\mathrm{and}\mathrm{one}\le p\le M-\mathrm{one};\end{array}$$

$${\alpha }_q=\{\begin{array}{c}\frac{\mathrm{one}}{\sqrt{N}},e\mathrm{from}l\mathrm{and}p=0;\\ \sqrt{\frac{2}{N}},e\mathrm{from}l\mathrm{and}\mathrm{one}\le p\le N-\mathrm{one.}\end{array}$$

The values of B _pq are called the DCT of the matrix U.

Reverse DCT is implemented according to the expressions:

$$U{}_{mn}={\alpha }_p{\alpha }_q{\displaystyle \sum _{p=0}^{M-\mathrm{one}}{\displaystyle \sum _{q=0}^{N-\mathrm{one}}{\alpha }_p{\alpha }_q{B}_{pq}\cos \frac{\pi (2m+\mathrm{one})p}{2M}\cos \frac{\pi (2n+\mathrm{one})q}{2N},(2)}}$$

where 0≤m≤M-1, 0≤n≤N-1;

$${\alpha }_p=\{\begin{array}{c}\frac{\mathrm{one}}{\sqrt{M}},e\mathrm{from}l\mathrm{and}p=0;\\ \sqrt{\frac{2}{M}},e\mathrm{from}l\mathrm{and}\mathrm{one}\le p\le M-\mathrm{one};\end{array}$$

$${\alpha }_q=\{\begin{array}{c}\frac{\mathrm{one}}{\sqrt{N}},e\mathrm{from}l\mathrm{and}p=0;\\ \sqrt{\frac{2}{N}},e\mathrm{from}l\mathrm{and}\mathrm{one}\le p\le N-\mathrm{one.}\end{array}$$

In the implementation of the JPEG compression algorithm, the original image after conversion from the RGB color space to YCrCb is divided into square blocks of size 8 × 8 or less 16 × 16, for which DCT is performed. The coefficients of discrete cosine transforms are filtered to remove some (depending on the degree of compression) values, quantized, and then encoded using a modified Huffman transform. As a result of these transformations, an array of data is obtained that is significantly smaller than the original image containing information from which it is possible to restore the original image with some accuracy, depending on the degree of compression. Image restoration occurs in the reverse order: first, the compressed image undergoes the inverse modified Huffman transform, then the inverse DCT. The disadvantage of DCT-based JPEG compression is the loss of image integrity resulting from specific “blocking” artifacts (contrast highlighting of 8 × 8 or 16 × 16 regions) in the reconstructed image. The artifact of “blocking” is a consequence of the lack of “smooth cross-linking” of the areas allocated for DCT. The next drawback is the loss of contrast, which is manifested in the “blurring” of the boundaries between different image objects and is a consequence of the filtering (removal during compression) of high-frequency components. The artifact of “blurring” is acceptable in photographic images, but in some types of images, such as satellite images, images for printing, where it is necessary to maintain contrast, “blurring” is unacceptable. When lossless compression in JPEG format, it is possible to maintain the contrast of the boundaries of objects, while the size of the compressed image remains large enough, which is also a drawback. JPEG format does not provide effective compression of images containing large spaces of the same color or smooth gradient.

The claimed invention eliminates the loss of integrity of the image, increases the compression efficiency of images containing large areas of the same tone or gradient (color, brightness), preserves the contrast of the borders between different image objects.

This problem is solved due to the fact that images (static or dynamic) are considered as discrete field structures, a complete numerical description of which (that is, values at all discrete points by the coordinates of space and (or) time) can be determined by solving the Laplace or Poisson equations, having initial data as boundary (boundary) conditions.

The essence of the invention lies in the fact that when compressing an image (static or dynamic), a data array is found that is called “pattern” in the framework of the invention, which is an array of boundary conditions and allows, with a given degree of accuracy, by numerically solving the Laplace or Poisson equations, to restore the original image . The resulting pattern contains a certain (in most cases quite significant) number of repeating elements and sequences, which allows you to effectively compress the pattern using standard methods, for example, based on a modification of the Huffman transform, or LZ78, or arithmetic coding. In the case of applying the Poisson equation for pattern formation and image restoration, the function of the right part is to be determined, the correct selection of which can greatly contribute to image compression.

The proposed method differs from JPEG methods in that it does not use spatial spectrum acquisition to compress the image, but rather the formation of boundary conditions for solving differential equations (Poisson or Laplace) that allow reconstructing the image. In this case, the spatial spectrum can be taken into account if the Poisson equations are chosen for pattern formation and image restoration, and if a function (or functional series) is included in the right side of the Poisson equation that allows one to take into account the spatial spectrum. Thus, the proposed method allows, while maintaining a small number of low-frequency components, to preserve small (high-frequency) image details due to the pattern of boundary conditions. The use of second-order differential equations allows you to track the change in changes (amplitude during the transition from point to point (from pixel to pixel), which describes the brightness, saturation or other characteristic of the image depending on the selected color scheme) and save only those values in which changes are significant, i.e. exceed numerically the specified value that determines the degree of compression. Thus, in contrast to JPEG-conversion for image compression and restoration, it is not the spatial spectrum of the image that is considered, but its spatial "differential structure", i.e. the presence and numerical value of the change changes, which allows you to effectively compress the gradation region (color, brightness, etc.) and in some cases produce more efficient compression compared to JPEG.

An image (static or dynamic) is considered as a spatially inseparable, multidimensional field structure. In the case of a static image - two-dimensional (analogue of a plane-parallel field), in the case of a dynamic image - three-dimensional (analogue of a three-dimensional field or plane-parallel field that changes in time). Thus, the image can be described by partial differential equations.

For the two-dimensional case:

- Laplace equation:

$$\frac{{\partial }^{2}U}{\partial x^2}+\frac{{\partial }^{2}U}{\partial {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000016.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}=0(3)$$

- Poisson equation:

$$\frac{{\partial }^{2}U}{\partial x^2}+\frac{{\partial }^{2}U}{\partial {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000016.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}=f(x,y)(\mathrm{four})$$

For the three-dimensional case (for dynamic images, video stream):

- Laplace equation:

$$\frac{{\partial }^{2}U}{\partial x^2}+\frac{{\partial }^{2}U}{\partial {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000016.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}+\frac{{\partial }^{2}U}{\partial {\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="00000016.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=0(5)$$

- Poisson equation:

$$\frac{{\partial }^{2}U}{\partial x^2}+\frac{{\partial }^{2}U}{\partial {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000016.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}+\frac{{\partial }^{2}U}{\partial {\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="00000016.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=f(x,y,t)(6)$$

where the following notation is used: x, y - spatial coordinates, t - third spatial coordinate or time, U - amplitude value in the component of the selected color space of the image, f - function connecting the patterns of image change with the change in spatial coordinates.

When compressing the image, the inverse problem to solving equations (3) - (6) is solved, that is, the boundary conditions are found. Such an array of boundary conditions within the framework of this invention is referred to as an image pattern or short pattern. In the case of choosing the Poisson equations, the function f is also to be found. After the pattern is formed, a standard compression method can be applied to it, applied to data arrays containing a significant number of repeating characters, for example, based on a modification of the Huffman transform, or LZ78, or arithmetic coding.

Unzipping a compressed image reduces to extracting the pattern (and function f in the case of Poisson equations) from the archive (based on the previously selected archiving method), then the Laplace or Poisson equations are solved based on known boundary conditions, for example, by the finite difference method.

The inventive method is illustrated by drawings, which depict:

figure 1 - possible choices of differentiation patterns for two-dimensional (x, y) and three-dimensional (x, y, t) spaces;

figure 2 - the original image is black and white with gradations of gray from 0 to 255, the length of the image array is 152100 bytes. The image contains small and large spatial elements;

figure 3 - visualization of an array of boundary conditions, called in the framework of the method "pattern", the pattern contains 42639 elements of the boundary conditions (non-zero) and 109461 zeros;

figure 4 - the result of image restoration for 20 iterations, according to the pattern (figure 3), without pre-filtering;

figure 5 - the result of image restoration for 20 iterations, according to the pattern (figure 3), using prefiltration;

6 is a graph of the sum of residuals for all points of the lattice, the nodes of which are the image pixels. On the vertical axis, the sum of the residual, on the horizontal iteration number. The graphs for the case of image restoration are displayed: using prefiltration; without applying prefiltration. Obviously, the use of prefiltration can accelerate the convergence of the iterative process many times, i.e. image recovery speed;

Fig.7 - the original full-color image 800 × 654, the number of bytes in the 24-bit palette - 1353600;

Fig - the pattern obtained for the RGB color palette, the number of significant bytes - 307358, zeros - 1046242. The ratio of the number of significant elements (bytes) of the pattern to the volume of the original image (bytes): 0.2271;

Fig.9 is a restored image according to the pattern (Fig.8), it is worth paying attention to the fact that despite a significant reduction in the amount of information, small (high-frequency) details (tablecloth texture) are preserved;

figure 10 - the pattern obtained for the YCrCB color palette, the number of significant bytes - 141449, zeros - 1212151, with approximately the same quality of the restored images (Fig.9 and Fig.11). The ratio of the number of significant elements (bytes) of the pattern to the volume of the original image (bytes): 0.1045. The number of significant elements is 2.17 times less than in the pattern in FIG. 8;

11 is a restored image according to the pattern (Figure 10). It is worth paying attention to the fact that despite a significant reduction in the amount of information, small (high-frequency) details (tablecloth texture) have been preserved;

Fig - one of the standard test images (The USC-SIPI Image Database http://sipi.usc.edu/database/), the original image is on the left (size, in bmp 24-bit format, 196608 bytes), restored - on right;

Fig - pattern for the image (Fig), the number of excluded elements (zeros) 134831;

Fig - one of the standard test images (in bmp 24-bit format), the size of 786432 bytes;

Fig - pattern for the image (Fig), the number of excluded elements (zeros) 535552;

Fig.16 is a restored image according to the pattern (Fig.15).

To disclose the method, consider the sequence of the compression procedure and the image recovery procedure. The compression procedure based on the Laplace equations consists in finding the boundary conditions for solving the partial differential equation (in accordance with the previously selected template). The choice of template depends on the specific implementation of the proposed method. Finding the boundary conditions (pattern) is done by calculating the values of the partial derivatives of the second order at each point in the image, followed by calculating the difference with the actual values at the corresponding point. The difference obtained is a criterion for making a decision to leave this point for the pattern or to exclude it, the numerical value of the criterion will correspond to the “degree” of compression. When the value of the criterion is zero, lossless compression occurs. For color images, conversion can be performed in any pre-selected color space, such as RGB or YCrCb. Conversion is done separately for each channel in the color palette. Special studies have shown that in the YCrCb color palette, for some images, a higher degree of compression can be achieved than in the RGB palette.

We write the entire procedure in a formal form for a two-dimensional static image with the selected template (Fig. 1). In the general case, the template can be of any configuration that allows one to efficiently solve partial differential equations. Let a two-dimensional image array be characterized by a set of values U _{x, y} , where x, y are the coordinates of the corresponding point. We will calculate the difference value of the actual value U _{x, y} , in the image array, and the result of solving the Laplace equation:

$$U_{x,y}-\frac{\mathrm{one}}{\mathrm{four}}(U_{x-\mathrm{one,}y}+U_{x+\mathrm{one,}y}+U_{x,y}-\mathrm{one}+U_{x,y+\mathrm{one}})=\Delta U_{x,y}$$

For the selected criterion h, we compare | ΔU _{x, y} | (absolute value) of the difference with the value h, if the condition (| ΔU _{x, y} | ≥h) is true, then U _{x, y} will be part of the pattern; if false, then U _{x, y is} excluded from the pattern and replaced by U _{x, y} , some (numerical) sign (for example, zero) is written by which it will be possible to determine that a given point with coordinates (x, y) is not a boundary condition, but requires calculation. Obviously, as a result of the calculations, there is a transition from integer values of U to floating-point values. This can be avoided by replacing the division operation with a bitwise shift operation. Solving a problem on a set of integers allows you to significantly speed up the process of forming a pattern. When choosing a practical implementation, it is necessary to take into account the conditions of specific tasks and the availability of computing resources.

(для векторов вдоль оси X) и $$\frac{d^{2}U}{d{y}^2}=0$$

(для векторов вдоль оси Y).It should be noted that the points located at the edges of the image (four vectors for a static two-dimensional image) are boundary conditions and the calculations described are not applied to them; it is possible to copy them directly to an array of boundary conditions or consider points located at the edges of the image as one-dimensional vectors to which equations of the form can be applied $$\frac{d^{2}U}{d{x}^2}=0$$

(for vectors along the X axis) and $$\frac{d^2\mathrm{<figure-callout\; id="2"\; label="U\; d\; y"\; filenames="00000016.png"\; state="\{\{state\}\}">U\; </figure-callout>}}{d{y}^{}}=0$$

(for vectors along the y axis).

In the case of a dynamic image, the principle approach remains the same. The equation for calculating the difference will have the following form:

$$U_{x,y,t}-\frac{\mathrm{one}}{6}(U_{x-\mathrm{one,}y,t}+U_{x+\mathrm{one,}y,t}+U_{x,y-\mathrm{one}},t+U_{x,y+\mathrm{one,}t}+U_{x,y,t-\mathrm{one}}+U_{x,y,t+\mathrm{one}})=\Delta U_{x,y,t}$$

To the planes bounding the region under consideration, the above-described method of forming a pattern for a two-dimensional image or direct copying into an array of boundary conditions can be applied.

When using the Poisson equation as the basis for calculating the pattern, the question arises of determining the right-hand side of the function f (x, y) for the two-dimensional case, f (x, y, t) for the three-dimensional case. The function f must be chosen so that the calculated pattern contains the smallest number of elements that are the boundary conditions. In this case, the function itself will be determined by a set of coefficients, the storage of which may require a significant amount of memory. The solution can be defined as minimizing the number of boundary elements forming the pattern and the coefficients of the function f while maintaining sufficient quality of the reconstructed image. Consider some options for the function f:

- plane: f (x, y) = ax + by + c;

is the inverse discrete cosine transform (see (2)), of the entire image space:

; $$f(x,y)={\displaystyle \sum _{p=0}^{M-\mathrm{one}}{\displaystyle \sum _{q=0}^{N-\mathrm{one}}{\alpha }_p{\alpha }_q{B}_{pq}\cos \frac{\pi (2m+\mathrm{one})p}{2M}\cos \frac{\pi (2n+\mathrm{one})q}{2N}}}$$

;

- a variety of wavelet functions, using a set of wavelet coefficients that allow you to calculate the values in the image space with a given accuracy;

- an array of discrete values corresponding to the average values in the areas obtained by dividing the image into rectangles (in the two-dimensional case) or parallelepipeds (in the three-dimensional case).

Obviously, any other functions (functional series) that are most suitable for a particular case can be selected as the right-hand side. As an example, consider the DCT in more detail. DCT, depending on the degree of image compression, allows you to save or exclude high-frequency ("small") details, and the proposed method can perfectly save "small" image details. Thus, several low-frequency DCT components can be used as the right-hand side of the Poisson equation. Similarly, you can use the wavelet transform as the right side of the Poisson equation, allowing you to take into account the features of the spatial spectrum of the image.

With a limited number of bits to save one channel of the color scheme, there is a limit on the possible values. For example, with eight bits per channel in the RGB color scheme, valid values are limited to a range of 0-255. The boundary values in the pattern are recorded by copying the corresponding values from the original image, other values in the pattern are filled with a pre-selected value, for example, zero. If a zero occurs at the points of the pattern, then it will be impossible to distinguish it from other zeros that record points that are not boundary conditions. For human perception, the gradation within 1/256 will be imperceptible, but if you need to be able to save the image without loss, then the error that needs to be corrected, you can use the image bit mask for correction.

As a result of the above transformations, a pattern is formed containing a significant number of repeating elements. Compression algorithms based on standard transformations such as Huffman, LZ78, and arithmetic coding can be effectively applied to such a pattern.

The inverse transformation is to restore the original image according to the pattern. The most obvious solution is to use the iterative finite difference method; the boundary conditions for the solution are the pattern. With this approach, the computation time for restoring an image in a sufficiently high quality can be significant, especially with large image sizes. Therefore, in the framework of the method under consideration, it is proposed to use prefiltration. The meaning of prefiltration is to accelerate the convergence of the process of iterative calculations by the finite difference method. Consider a possible implementation of prefiltration, for example, a two-dimensional image. Prefiltration is performed sequentially first in the X direction, and then in the Y direction, or vice versa. So, let’s go through the first (the first of those to which the difference method of patterning was applied, extreme lines are boundary conditions, see above) line, if we meet an element that is an element of the boundary condition, remember its value and move on until we meet the next element, which is an element of the boundary condition. Knowing the value of two boundary elements within the same vector, we use an approximation (for example, linear) to calculate the values of the elements located between them. Thus, we approximate all the values within the same row. Successively go through all the lines in the X direction, and then make the same passage along all the lines in the Y direction. When passing through the lines in the Y direction, we take into account the previously obtained values (when passing along X) and calculate the actual value as the average between the passage in the X direction and Y.

It is possible to add pre-filtering passes along the diagonals.

When using the Poisson equations as a function that performs “pre-filtering”, the right-hand side equation can be used together with the passage described above in the X and Y directions.

The result of this pre-filtering is a data array that can be considered as part of the calculations obtained as a result of performing some iterative approximation. The pre-filtering described above can significantly accelerate the convergence of the iterative process, and therefore, accelerate the image recovery process. Further iterative calculations can be performed using the finite difference method. The criterion for completing the calculations can be a numerical estimate of the residual. This approach allows you to quickly create an image (for example, on a monitor screen) and sequentially, continuing iteration and periodically updating the image, to increase its visual quality (progressive decoding).

The described method can be applied to dynamic (three-dimensional) images using the time f (x, y, t) as another coordinate. It is possible to use the method in other multidimensional images, for example, in three-dimensional television, where, depending on the implementation, there may be four (three spatial and time) and more coordinates.

To implement the proposed method, it is necessary to perform a sequence of actions that meets all the signs of the algorithm.

The order of the sequence of actions of the method is strictly defined and determined.

A generalized compression algorithm for a two-dimensional static image (the Laplace equation is applied). In the description of the algorithm, the image, pattern - are integer, two-dimensional arrays of values (in the nodes of the image grid - pixels).

1. We form an image pattern, which is an array of boundary conditions for solving the Laplace or Poisson equations during restoration. If the Poisson equation is applied, we calculate the necessary coefficients that uniquely describe the right side of the Poisson equation.

2. If it is necessary to save the image without loss, we form a bit matrix (array) that allows for image correction during restoration. The bitmask is also compressed, for example, by encoding the lengths of the RLE series.

3. We apply the standard compression method to the resulting pattern, which allows us to efficiently compress data containing a significant number of repeating elements.

Generalized image recovery algorithm:

1. We perform the operation of unzipping the pattern in accordance with the method of its packaging. If necessary, we unzip the coefficients (in the case of using the Poisson equation) and the bit matrix (to restore the image without loss).

2. We perform prefiltration using the pattern learned in (clause 1). The purpose of prefiltration is to accelerate the convergence process of the iterative process of image restoration according to the pattern.

3. We calculate (restore) the image according to the pattern, using the array obtained at the prefiltration stage as the recovery area (array in which the restored image will be received). The criterion for the end of the calculations may be a given number of iterations or the value of the residual (controlling the convergence of the iterative process).

4. In case it is necessary to restore the image without loss, we perform the correction using a bit mask.

Thus, the proposed method eliminates the loss of image integrity, increases the compression efficiency of images containing large areas of the same tone or gradient (color, brightness), and maintains the contrast of the borders between different image objects.

Claims (2)

1. The method of image compression, based on the exclusion of some part of the information, characterized in that the information is excluded from the spatial domain by numerically solving the Poisson or Laplace differential equations and then evaluating the difference between the obtained solution and the actual values at discrete points of the image, form an array of boundary conditions, containing a significant number of equal elements, which are compressed, and differential equations in partial derivatives of Pua are solved to restore the image Sson or Laplace using an array of boundary conditions. 2. The method according to claim 1, characterized in that the array of boundary conditions is prefiltered by filling in the set of image points not belonging to the boundary conditions with approximation function values calculated from known points of the boundary conditions.

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