WO2010030256A1

WO2010030256A1 - Alias-free method of image coding and decoding (2 variants)

Info

Publication number: WO2010030256A1
Application number: PCT/UA2009/000006
Authority: WO
Inventors: Denis Afanassyev; Alexander Palash; Sergey Svichkarev
Original assignee: Tovaristvo Z Obmezenou Vidpovidalnistu 'smail'
Priority date: 2008-09-12
Filing date: 2009-02-11
Publication date: 2010-03-18
Also published as: UA91591C2

Abstract

The present invention relates to image processing and in particular to the coding and decoding of images represented in a digital form. An alias-free method of image coding and decoding for preventing the appearance of aliases (coherent artifacts) in the restored image obtained after decoding with simultaneous enhancement of the lossless and lossy compression efficiency and quality of the restored image by means of providing the random noise-like nature of lossy decoding error within the definite limit depending on the compression ratio to be achieved. The proposed method of alias-free image encoding and decoding can be used, for instance, for medical images as well as ones obtained in scientific experiments for applications requiring the high-quality images completely free from the false detail, and for enhancing the quality of the decoded images and simplifying the coding and decoding procedures due to the absence of special methods of image structure analysis

Description

Alias-free method of image coding and decoding (2 variants)

Field of the invention

The present invention relates to image processing and in particular to the coding and decoding of images represented in a digital form. Background of the invention

Image processing comprises generation of the selected array of data from the input one, compression of the said array for its more efficient storage, for instance, in the computer memory, and further use of the selected data array for reconstruction of the image, for instance, on the paper or display screen. Coding of the images obtained with use of an input device, for instance, a video or still camera, or an image scanner is used for removing the extra data unnecessary for reconstruction of the input image with sufficient quality. When the coding process achieves high compression, certain part of the input image information may be lost. This lost part may be either usable information about the image details or a mixture of noise and aliases contained in any image represented in a digital form. The initial signal to noise ratio of an input image is always finite due to the noise generated by an input device. Image decoding is used for reconstruction of the input image from the encoded one and comprises the inverse operations in respect to ones used during image coding. It is known that any digital conversion of a continuous (analog) signal with the use of an input device, for instance, a digital conversion of a natural image by means of a photo camera or a scanner, is associated with generation of aliases. These aliases appear due to the failure to fulfill the conditions of the Sample Theorem (see R. Cook, "Stochastic Sampling in Computer Graphics" ACM Transactions on Graphics, Jan. 1986, pp. 51-72, pp. 52, 53). The image aliases are the new elements or structures not present in a natural input image, but are visible on its digital representation and possess clearly recognizable nonrandom origin. The aliases are visible on images printed or displayed by means of any output device. They impair the image quality and can grow during subsequent image processing. A ladder structure on lines or edges is an example of such aliases. The usual way for suppressing of aliases is, for example, the use of pre- or postfiltering of the image with a known transfer function or a combination of both (M. Dippe and E. Wold. Antialiasing through Stochastic Sampling. In Computer Graphics (SIGGRAPH' 85 Conference Proceedings), pp. 69-78, 1985, p. 69).

It is worth noting that a usual requirement for using the said methods is to keep the aliases intensity within the preset margin while increasing the compression rate of the input image.

Description of the prior art The claimer knows many methods of image coding and decoding, among which the closest ones are the following.

A known method of image coding and decoding, providing the lossy compression of the images is developed by JPEG (Joint Photographic Experts

Group) (http://www.jpeg.org/). This method is widely used and comprises the following: dissection of an input image represented by a set of luminance amplitudes and a set of chrominance ones into a number of equal rectangle areas, each area being a 8x8 pixels matrix, performing the discrete cosine transform on each such matrix to obtain the set of DCT coefficients based on the set of color amplitudes. Then the computed DCT coefficients are quantized to reduce the resulting information volume. Next, the array of quantized DCT coefficients is losslessly compressed using, for instance, a Huffman or arithmetic coding algorithm. The decoding algorithm comprises the inverse operations.

The quantizing of the DCT coefficients results in abandoning of high- frequency content of the information on the color amplitudes. This allows one to get a high degree of image compression, although with certain loss of image detail. Simultaneously the compression and decompression processes run fast. Indeed said partial loss of information results in the generation of aliases of various look, for instance, the block artifacts. Therefore, the generation of aliases prevents using the JPEG method in some critical applications, for instance, in medicine or geophysics, where there is a need of high-quality images usable not only for simple visual observation, but also for further analysis with extracting the valuable information from them (for instance, X-ray and satellite images). Such applications generally require the use of formally lossless methods of image coding and decoding. For instance, a known method of image coding and decoding, JPEG-LS

(http://www.jpeg.org/jpeg/jpegls.html), performs a lossless coding and decoding and includes an option of compression with small losses as well. This method is based on a LOCO-I algorithm (LOw Complexity Compression for Images) (M. Weinberger, G. Seroussi, G. Sapiro, "The LOCO-I Lossless Image Compression Algorithm: Principles and Standardization into JPEG-LS", Hewlett- Packard Laboratories Technical Report No. HPL-98-193R1, November 1998, revised October 1999. IEEE Trans. Image Processing, Vol. 9, August 2000, pp. 1309-1324).

This method comprises forming a base image model by interpolation of color amplitude of a current pixel by interpolation on the subset of color amplitudes of previously processed pixels, for instance, two adjacent ones, forming the array of error between the said base model and input image and coding this error by means of Golomb-Rice code. The methods of image structure analysis and context model formation using the extra detail information are also used during formation of the base model thus complicating the said method. The methods of context model formation are not universal for different kinds of images. Additionally, the use of the said method in the applications requiring totally alias- free images, like medical ones (resulting in large image files) leads to a huge growth of digital storage capacities of medical centers, reaching hundreds terabytes per year, which cannot be further tolerated.

The method of lossless image coding and encoding using the entropy coding is known. This method comprises forming a base image model on color amplitudes of current pixels by interpolation of color amplitudes of previously processed ones with a preset rule of scanning of the whole pixels of the input image. Then the error array is formed by computing the differences between the interpolated color amplitudes of the base model pixels and those of the input image ones. Thin the computed error values are converted to the binary code and the repeating series of zeroes are detected and partially abandoned. A code describing the quantity of repeating nonzero error values is generated for the rest of the error array. (Application WO 2006/010644, published July 04, 2007).

Also a method of image coding and decoding is known, that comprises performing the interpolation of pixels color amplitudes using a subset of pixels adjacent to the current one, to build a base image model.

Further the subset of adjacent pixels is quantized using the given quantization factor and the general error is computed for each said quantized subset. The code table based on the computed error values is formed for each said subset and the error values are encoded using the restored error values for the current pixel from the code table. The image is restored during decoding by adding the current pixel values and the error ones taken from the code table with the use of the same subsets of adjacent pixels that ones used during the encoding (Patent JVs US 5 680 129, issued October 21, 1997).

The next known method of image coding and decoding includes the similar to above described procedures of base model formation and error data array computation. The interpolation is performed over the previously defined subparts (mostly rectangle ones) of an image to be encoded, and the error data array is kept within a preset limit by a comparison of error value with a given boundary and subsequent division of a current subpart into smaller ones until a smallest preset subpart size is reached (Patent Xs US 4 791 486, issued December 13, 1988). This method allows one to limit the error values thus reducing the output file size during image encoding. Indeed, the restored image decoded by this method still contains the coherent error components (aliases) compromising the image quality. Also the subsequent repeating of this coding and decoding procedure the said aliases build up, therefore the possible application areas exclude ones requiring the absence of such added aliases, for instance, the already mentioned storage and processing of medical and geophysical images. The mentioned known methods of image coding and decoding do not add the new aliases when used for lossless compression by definition. Indeed, these methods do not allow one to remove the aliases already present in the input image and not always are equally efficient by quality to compression ratio relationship during lossy compression.

The following method of lossy coding and decoding of the images is prior art method. This method comprises the formation of pixels subset for an input bitmap image obtained, for instance, by scanning and stored in a computer memory. The subset contains the pixels of a column or a row, accordingly to the image scanning direction. Then the limit error value is set. The first and last pixel is defined for each selected subset and the base image model is formed by interpolation using the first pixel and the ones forming a line or a curve together with the said first pixel. Then the error between the interpolated and input images is computed and compared with preset limit error value. If the computed error value exceeds the preset limit, the above actions are performed in respect to the corresponding pixel until the last pixel of each subset is reached. Finally, the values of first and last pixels and distances between them are entropy coded and stored in the output file, and the error data array is reduced (Patent JVb US 5 245 679, issued September 14, 1993, Int. Cl: G06K9/36, G06K9/46). This method is simple for implementation, but it does not allow one to remove or reduce the appearance of aliases during image coding. The image quality rapidly deteriorates with increase in compression ratio using lossy compression according to this method, thus limiting the possible applications.

Summary of the invention It is an object of the present invention to provide a method of image coding and decoding for prevention of the appearance of aliases (coherent artifacts) in the restored image obtained after decoding with simultaneous enhancement of the lossless and lossy compression efficiency and quality of the restored image by means of providing the random noise-like nature of lossy decoding error within the definite limit depending on the compression ratio to be achieved. This object of the invention can be achieved by providing an alias-free method of image coding, comprising the steps of: setting up the size of a subset of randomly selected pixels; generating an array of coordinates of randomly selected pixels; - forming a subset of randomly selected pixels on the basis of the generated array of coordinates; forming an image base model by interpolating color amplitudes on the subset of randomly selected pixels; forming an array of error data by calculating the difference between the color amplitudes for an image and those for the base model; archiving the array of error data; recording as a file the archived array of error data, the subset of randomly selected pixels and the coordinates of the randomly selected pixels or parameters of the generated array of coordinates of randomly selected pixels. This object of the invention can be also achieved by providing a method of image decoding, comprising the steps of: opening the file and restoring the archived error data array; forming an image base model by interpolating color amplitudes using the same interpolation technique as in image coding; - forming a restored image by summarizing of interpolated color amplitudes with error values of restored error data array.

In alternative embodiment of the present invention the alias-free method of image coding, coded by the previous alias-free method of image coding, comprising the steps of: - setting up the size of a subset of randomly selected pixels; generating an array of coordinates of randomly selected pixels; forming a subset of randomly selected pixels on the basis of the generated array of coordinates; forming an image base model by interpolating color amplitudes on the subset of randomly selected pixels; forming an array of error data by calculating the difference between the color amplitudes for a physical image and those for the base model; - forming a reduced array of error data by: setting up an error boundary value and a quantization factor; - comparing error values of array of error data, by their absolute value, with the preset error boundary value;

- assigning a zero value to those error values of array of error data, which, by their absolute value, do not exceed the error boundary value;

- generating a set of random noise values by means of a programmed random number generator;

- summarizing error values of array of error data, which, by their absolute value, exceed the error boundary value, with the set of random noise values;

- quantizing the obtained summarized values using the preset quantization factor; archiving the reduced array of error data; recording as a file the archived reduced array of error data, the subset of randomly selected pixels and the coordinates of randomly selected pixels or parameters of the.generated array of coordinates of randomly selected pixels. In alternative embodiment of the present invention the method of image decoding, coded by the previous alias-free method of image coding, comprising the steps of: opening the file and restoring the archived reduced error data array; restoring the reduced array of error data by multiplying it by the quantification factor used in image coding and subtracting the set of random noise values generated by means of the random number generator; forming an image base model by interpolating color amplitudes on the subset of randomly selected pixels using the same interpolation technique as in image coding; forming a restored image by summarizing of interpolated color amplitudes with error values of restored error data array.

In a preferred embodiment of the both alias-free method of image coding the subset of randomly selected pixels can be formed by dividing an input image into a set of identical elementary areas having common boundaries, setting up a common rule of pixel skipping in said elementary areas and selecting a single pixel in each of said elementary areas with the coordinate of said single pixel being selected from the previously generated set of random numbers. The said identical elementary areas can be rectangles. Additionally, the rule of pixel skipping in the elementary areas is set up by sequential scanning of pixels associated with each of the elementary areas from left to right and from top to bottom.

The interpolation when forming the image base model can be carried out using the Delaunay triangulation. Further, the subset of randomly selected pixels and the coordinates of randomly selected pixels can be archived coincidently with archiving the array of error data.

Additionally, coordinates of randomly selected pixels can be corrected at forming a subset of randomly selected pixels, a multilevel representation of the array error values can be carried out and nonlinear quantization can be used for error reducing.

A synchronization parameter for the random number generator, for instance, a code word can be used as a parameter for generating an array of randomly selected pixels. A reference to a preset table of coordinates of randomly selected pixels located in a separate file on the physical data carrier can be used as the parameter for generating an array of randomly selected pixels.

A method of decoding of an image, encoded by the above method of image coding according to the present invention may comprises opening the stored image file, restoring the archived error data array, subset of randomly selected pixels and their coordinates. Also the coordinates of the randomly selected pixels can be computed with the use of synchronized generator of random numbers or determined by reference to the previously computed preset table.

Additionally, a restored image can be postfiltered. There is a following cause-effect relation between the critical limitations of the alias-free method of image coding and decoding that is claimed, and the said objects of the invention can be achieved.

The inventors have found during the investigation of the problem state of the art that there exist the theoretical studies on the use of the stochastic (random) sampling in the coding process for reducing the aliases in the restored image after its decoding. For instance, a problem of conversion of a coherent error or aliases into a random noise with its amplitude gradually increasing with compression factor has been studied in a paper by M. Dippe and E. Wold [Antialiasing through Stochastic Sampling. In Computer Graphics (SIGGRAPH' 85 Conference Proceedings), pp. 69-78, 1985]. Therefore the residual error of lossy coding of an image can be made similar to the grain and blur usually observed in conventional analog (chemical) photography.

The inventors have found during previous experiments the following.

The forming of the base image model using the stochastic pixel sampling together with archiving an array of error data, forming a file for image information storing, comprising the array of error data, subset of randomly selected pixel, coordinates of randomly selected pixel, forming of the reduced array of error data by setting up an error boundary value and a quantization factor, comparing error values of array of error data, by their absolute value, with the preset error boundary value, assigning a zero value to those error values of array of error data, which, by their absolute value, do not exceed the error boundary value, generating a set of random noise values by means of a programmed random number generator, summarizing error values of array of error data, which, by their absolute value, exceed the error boundary value, with the set of random noise values, quantizing the obtained summarized values using the preset quantization factor allows to transformation coherent constituent of error spectrum in a noise-type spectrum and to keep off the appearance of block aliases and ladder aliases in the restored image. A sited character also allows performing partial or full transformation of said aliases in a noise-type spectrum. The use of randomly selected subset of pixels by means of setting of the subset size, generation of the array of random pixel coordinates, formation of the subset of the randomly selected pixels using the generated coordinates array, allows one to avoid the aliasing of the base model of the image, simultaneously making the error between the input image and the base model similar to the random noise. The resulting error array will not possess a regular structure, which can be clearly observed as aliases, for instance, blocks, ladders or more. The goal of using the random selection of the pixels is the building of a base image model containing a minimal redundancy, according to the Sample Theorem (Whittacker, Nyuquist, Kotelnikov, Shannon). In contrary to the known methods of image coding and decoding, for instance, the above described JPEG one, an aliased part of the input image, which is formed during its primary digitizing (the coherent error spectrum) is substituted by a random noise during the decoding, and the amplitude of this noise gradually increases with the compression degree. The upper limit of this noise is determined by the adopted image quality and can vary dependent on the application of the restored images.

The random selection of the pixels by means of dividing the input image into the set of equal elementary areas with common boundaries, setting a general skipping rule and choosing a single pixel within each such region with a coordinate taken from a previously generated array of random numbers makes it possible to guarantee that a single pixel per elementary area is selected and the mean density of the selected pixels over a number of the elementary areas will be equal to that over the whole image, and to simplify the task of selection an storage of the random pixels coordinates during the image coding and their extraction during the decoding. It is shown [M. Dippe and E. Wold. Antialiasing through Stochastic Sampling. In Computer Graphics (SIGGRAPH' 85 Conference Proceedings), pp. 69-78, 1985] that the use of different stochastic distributions (for instance, Poisson distribution, p. 71, fig 2, 3 or dithered one, p. 72, fig 4, 5) allows one to control the signal to noise ratio an the resolution of the resulting image. The color amplitudes of the rest of pixels forming the base image model are computed by interpolation of the color amplitudes of the pixels from the randomly selected subset. The use of Delaunay triangulation for this purpose allows one to apply some smoothing of the fine detail in the model due to its inherent low-pass filtering. Error data array reduction by the above described method results in a reproduction of the initial error values with a predetermined accuracy, which depends on the reduction parameters, such as the error threshold and quantization factor. The spectrum of the resulting residual error is close to that of a random noise and is virtually similar to one taking place in the analog methods of image storage and representation. As far as any natural image contains some amount of noise (as it was already mentioned), the additional noise introduced during the error data array reduction will be visually undistinguishable up to a certain limit. The restored image will nevertheless preserve a lot of fine detail, or some detail will encounter a controlled minor blur. The noise (dither) introduced during the error reduction is needed only for smoothing the quantization error, especially at the bottom of the dynamic range of the color amplitudes. Therefore this dither can be removed during the error archiving that result in appearance of large sequences of zero values in the error array thus substantially increasing the compression efficiency. This dither is substituted by a generated noise during the image decoding.

One should note, that the resulting accuracy of the error restoration depends on the preset error threshold and quantization factor and thus can be easily predicted.

These preset values of the error threshold and quantization factor make it possible to keep the residual mean square error of the image restoration during decoding within the predicted margin, what simplifies the implementation of the coding and decoding method. There is no need to employ additional procedures for observing the necessary restoration accuracy like ones used in the above described known methods. The further increase in compression efficiency together with optimizing the processing speed is possible by using the multilevel error representation.

The error data to be stored can be further minimized by correcting the coordinates of the randomly selected pixels during image coding.

Detailed description of a proffered embodiment The input digital bitmap image is generally represented by a matrix of

[b (i, j)], where is a number of pixels in a row, j is a number of pixels in a column. A size of a subset of randomly selected pixels is set for such an image. This size is limited by number of pixels of an input image and the necessary accuracy.

The input image is then divided by a number of equal elementary areas with common boundaries. These elementary areas can be, for instance, the rectangles. Then the general skipping rule for these elementary areas is set. This skipping rule comprises, for instance, a sequential scanning of the pixels of an elementary area, from left to right and from top to bottom.

Next, the coordinates for the pixels in these elementary areas are set. The array of randomly selected coordinates is then generated on the base of the above ones.

A single pixel per elementary area is selected according to the previously generated coordinates, using the above skipping rule in every elementary area. As a result, the subset of randomly selected pixels is formed. At the next step the color amplitudes for the rest of pixels are interpolated on the base of the randomly selected subset. The interpolation method can be, for instance, the Delaunay triangulation. For this purpose the subset of the randomly selected pixels, which represents a characteristically surface of the color amplitudes, is divided into a number of elementary triangles with common boundaries. An approximation of the said characteristically surface is defined inside each said elementary triangle as a plane fragment. The coefficients of a, b and c for the equation of / (x, y) = ax + by + c for this plane fragment are computed locally for each said elementary triangle by solving a linear system of equations. Such interpolation possess the properties of a low-pass filter that smoothes the fine image details. One can also use other interpolation methods like the method of nearest neighborhood, bilinear, biquadratic, bicubic, B-spline, Lagrange, etc.

The base image model is then formed from the interpolated and randomly selected pixels. Then the error between the color amplitudes of the base model pixels and the input image ones is computed. The subset of correlated pixels can be formed within the randomly selected ones to minimize the error.

The differences obtained form the error data array. This array is archived at the next step of the coding process by means of the known archiving methods, for instance, the Huffman algorithm, the run length encoding (RLE). Additionally, the subset of randomly selected pixels and theiδr coordinates can be archived as well in the different embodiments of the proposed method.

Finally the error data array, subset of randomly selected pixels and coordinates of randomly selected pixels are written to a file, which is then stored in any storage device, for instance in the computer memory, hard disk drive, etc. The image decoding is performed by an inverse process using the same parameters that ones used during the image coding. The image file is opened and the archived data are extracted. Then the base image model is formed by the interpolation of the color amplitudes of the randomly selected pixels subset using the same interpolation method as during the image coding. Next the color amplitudes of the base model pixels are summarized with the values from the error data array and the input image is restored.

This method of image coding and decoding provides the lossless compression and the restored image is completely identical to the input one.

The lossy image coding according to the present embodiment comprises the above steps in the same sequence, but after the formation of the error data array, the said array is reduced. The reduction of the array of error data is performed the following way. First, the error reduction parameters such as the error threshold and the quantization factor are set at the first stage of the encoding process together with the size of the subset of randomly selected pixels. Then the error values are compared with the error limit by their absolute values. The zero values are assigned to those error values, which are lower than the said threshold. The generated random noise (dither) is then added to the error values, which are above the said threshold. Further, these error values with added dither are divided by said the quantization factor. The decoding of the image after the above described lossy compression additionally comprises the restoring of the reduced error by means of multiplying the reduced error values by the quantization factor used during the image coding and subtracting the synchronized dither. The dither synchronization can be achieved, for instance, by using the same initial value at starting the random numbers generator. The range of generated random numbers is defined at the image coding to set the dither amplitude.

The reduction of the error data array can be performed by nonlinear quantization according by one of the known methods. In this case the corresponding set of parameters is used together with the inverse method during the image decoding.

The lossy compression may include the multilevel error coding. For this purpose the randomly selected subset is formed within the obtained error data array, and the size of this subset is larger than a size of the said subset of the randomly selected pixels. The next level of the error representation is then formed on the base of the said randomly selected subset of the error data array. This error subset is also processed using the preset error threshold, linear or nonlinear quantization with corresponding parameters. As a result, the reduced error subset contains more zero sequences and can be better archived. It is possible to repeat these steps further several times. Therefore it is possible to form a subset of randomly selected pixels with minimal redundancy. The correction of the coordinates of randomly selected pixels may be used after the formation of the error data array for further enhancement of the coding efficiency. This correction may be performed, for example, the following way.

First, a single pixel different from the randomly selected one, is selected in every elementary area. Previously the region, containing a number of adjacent elementary areas and an error limit for such region are set. Then a subset of randomly selected pixels from a number of elementary regions is formed and the error statistics over this subset is analyzed by means of building the histogram based on the computation of the root mean square (RMS) and peak error values and their comparison with the preset limit. Next, the elementary areas where the error values exceeding the said limit are maximal are determined and other pixels are selected in those areas in order to reduce the error. Then the corrected coordinates of the selected pixels are used in the coding process and written to the file. The size of the subset of randomly selected pixels remains the same. Therefore the correction of the coordinates of the randomly selected pixels is aimed for reduction of the error statistical distribution that results in the enhancement of the error archiving efficiency.

Brief description of the drawing

The examples of the execution of alias-free method of image coding and decoding are given in the following figures.

Figs 1 and 9 are the initial color images without compression. Figs 2 and 4 are images which received as result of lossy compression with the preset error threshold equal to 4 and quantization factor equal to 4.

Figs 3 and 11 are images which received as the result of lossy compression with the preset error threshold equal to 8 and quantization factor equal to 8.

Figs 4 and 12 are image based on the array of the error value, which is formed by carrying out of the image compression shown in Figs 1 and 9 correspondingly, with the preset error threshold equal to 4 and quantization factor equal to 4. Figs 5 and 13 are images based on the array of the error value, which is formed by carrying out of the image compression shown in Figs 1 and 9 correspondingly, with the preset error threshold equal to 8 and quantization factor equal to 8. Figs 6 and 14 are enlarged subimages shown in Figs 1 and 9. Figs 7 and 15 are enlarged subimages shown in Figs 2 and 10. Figs 8 and 16 are enlarged subimages shown in Figs 3 and 11. Aliasing artifacts such as «jaggies» on the edge of the objects shown in the image 6, 7, 8, 14, 15, 16, are appears at transformation physical (original) image in a digital form. The photos shown clearly demonstrate the absence of the coherent components (aliases) in the error of the lossy compressed images and their substitution by the random noise, which looks like a blur. Also evident is the dependence of the fine detail content on the preset values of the error threshold and quantization factor for the image compression. One should note that these images are of relatively low resolution (512x512 pixels), what shows the efficiency of the present method even for so small size. Moreover, one can expect much higher efficiency of this method for large images typically used in the above described applications not only for visual observation.

Statement of the advantages to be gained by the invention The proposed method of alias-free image encoding and decoding by converting the coherent error spectrum (alias content) into the random noise provides the absence of aliases during the compression of the digital images and can be used, for instance, for medical images as well as ones obtained in scientific experiments for applications requiring the high-quality images completely free from the false detail, and for enhancing the quality of the decoded images and simplifying the coding and decoding procedures due to the absence of special methods of image structure analysis.

Claims

CLAIMS (2 variants)

1. An alias-free method of image coding comprising, for an image recorded as a bitmap file: setting up the size of a subset of randomly selected pixels; - generating an array of coordinates of randomly selected pixels; forming a subset of randomly selected pixels on the basis of the generated array of coordinates; forming an image base model by interpolating color amplitudes on the subset of randomly selected pixels; - forming an array of error data by calculating the difference between the color amplitudes for an image and those for the base model; archiving the array of error data; recording as a file the archived array of error data, the subset of randomly selected pixels and the coordinates of the randomly selected pixels or parameters of the generated array of coordinates of randomly selected pixels.

2. An alias-free method of image coding comprising, for an image recorded as a bitmap file: setting up the size of a subset of randomly selected pixels generating an array of coordinates of randomly selected pixels; - forming a subset of randomly selected pixels on the basis of the generated array of coordinates; forming an image base model by interpolating color amplitudes on the subset of randomly selected pixels; forming an array of error data by calculating the difference between the color amplitudes for a physical image and those for the base model; - forming a reduced array of error data by: setting up an error boundary value and a quantization factor; - comparing error values of array of error data, by their absolute value, with the preset error boundary value; - assigning a zero value to those error values of array of error data, which, by their absolute value, do not exceed the error boundary value;

- generating a set of random noise values by means of a programmed random number generator; - summarizing error values of array of error data, which, by their absolute value, exceed the error boundary value, with the set of random noise values;

- quantizing the obtained summarized values using the preset quantization factor; - archiving the reduced array of error data; recording as a file the archived reduced array of error data, the subset of randomly selected pixels and the coordinates of randomly selected pixels or parameters of the generated array of coordinates of randomly selected pixels.

3. The alias-free method of image coding according to Claim 1 or Claim 2, wherein the subset of randomly selected pixels is formed by dividing an input image into a set of identical elementary areas having common boundaries, setting up a common rule of pixel skipping in said elementary areas and selecting a single pixel in each of said elementary areas with the coordinate of said single pixel being selected from the previously generated set of random numbers.

4. The alias-free method of image coding according to Claim 3, wherein said identical elementary areas are rectangles.

5. The alias-free method of image coding according to Claim 3, wherein the rule of pixel skipping in the elementary areas is set up by sequential scanning of pixels associated with each of the elementary areas from left to right and from top to bottom.

6. The alias-free method of image coding according to Claim 1 or Claim 2, wherein when forming an image base model, interpolating is carried out using the Delaunay triangulation.

7. The alias-free method of image coding according to Claim 1 or Claim 2, wherein the subset of randomly selected pixels and the coordinates of randomly selected pixels are further archived coincidently with archiving the array of error data.

8. The alias-free method of image coding according to Claim 1 or Claim 2, wherein at forming a subset of randomly selected pixels coordinates of randomly selected pixels are corrected.

9. The alias-free method of image coding according to Claims 1, 2, wherein a multilevel representation of the array error values is carried out.

10. The alias-free method of image coding according to Claim 2, wherein error reduction is carried out using nonlinear quantizing.

1 1. The alias-free method of image coding according to Claim 1 or Claim 2, wherein a synchronization parameter for the random number generator is used as the parameter for generating an array of randomly selected pixels.

12. The alias-free method of image coding according to Claim 1 or Claim 2, wherein a reference to a preset table of coordinates of randomly selected pixels located in a separate file on the physical data carrier is used as the parameter for generating an array of randomly selected pixels.

13. A method of image decoding comprising, for an image, coded by the method of image coding according to Claim 1 : opening the file and restoring the archived error data array; - forming an image base model by interpolating color amplitudes using the same interpolation technique as in image coding; forming a restored image by summarizing of interpolated color amplitudes with error values of restored error data array.

14. A method of image decoding comprising, for an image, coded by the method of image coding according to Claim 2: opening the file and restoring the archived reduced error data array; restoring the reduced array of error data by multiplying it by the quantization factor used in image coding and subtracting the set of random noise values generated by means of the random number generator; forming an image base model by interpolating color amplitudes on the subset of randomly selected pixels using the same interpolation technique as in image coding; forming a restored image by summarizing of interpolated color amplitudes with error values of restored error data array.

15. The method of image decoding according to Claim 13 or Claim 14, wherein the image file is opened and the archived array of error data, the subset of randomly selected pixels and the coordinates of randomly selected pixels are restored.

16. The method of image decoding according to Claim 13 or Claim 14, wherein the coordinates of randomly selected pixels are calculated by means of a synchronized random number generator.

17. The method of image decoding according to Claim 13 or Claim 14, wherein the restored image is post-filtered.