Lossless Discrete Atomic Compression of Full Color Digital Images

Makarichev, Viktor; Brysina, Iryna

doi:10.1109/cadsm52681.2021.9385239

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…Comparing (10) with (15), we conclude that the algorithm, which is developed above, has much less time complexity. In other words, the proposed algorithm provides faster computation of ups-function values.…”

Section: Dynamic Algorithm For Computation Of Atomic Functions Ups(x)mentioning

confidence: 91%

“…Its main idea can be described as follows [16]: if process of some problem solving contains many identical subproblems, then complexity can be reduced by storing their solutions in memory to avoid solving them multiple times. It is this approach that can be applied to development of s upvalues computation algorithm with complexity, which is less than (10).…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…A set of fundamental results, which were obtained by V. O. Rvachev and representatives of his scientific school, provided the successful application of atomic functions to different processes and phenomena modeling [5,6], as well as lossy compression of digital images [7,8]. Also, it was shown in [9,10] that lossless and near-lossless image compression can be obtained. A combination of convenient properties makes it promising to apply atomic functions to the development of high-performance data analysis and processing algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Application of dynamic programming approach to computation of atomic functions

Makarichev

Kharchenko

2021

reks

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The special class of atomic functions is considered. The atomic function is a solution with compact support of linear differential functional equation with constant coefficients and linear transformations of the argument. The functions considered are used in discrete atomic compression (DAC) of digital images. The algorithm DAC is lossy and provides better compression than JPEG, which is de facto a standard for compression of digital photos, with the same quality of the result. Application of high precision values of atomic functions can improve the efficiency of DAC, as well as provide the development of new technologies for data processing and analysis. This paper aims to develop a low complexity algorithm for computing precise values of the atomic functions considered. Precise values of atomic functions at the point of dense grids are the subject matter of this paper. Formulas of V. O. Rvachev and their generalizations are used. Direct application of them to the computation of atomic functions on dense grids leads to multiple calculations of a great number of similar expressions that should be reduced. In this research, the reduction required is provided. The goal is to develop an algorithm based on V. O. Rvachev’s formulas and their generalizations. The following tasks are solved: to convert these formulas to reduce the number of arithmetic operations and to develop a verification procedure that can be used to check results. In the current research, methods of atomic function theory and dynamic programming algorithms development principles are applied. A numerical scheme for computation of atomic functions at the points of the grid with the step, which is less than each predetermined positive real number, is obtained and a dynamic algorithm based on it is developed. Also, a verification procedure, which is based on the properties of atomic functions, is introduced. The following results are obtained: 1) the algorithm developed provides faster computation than direct application of the corresponding formulas; 2) the algorithm proposed provides precise computation of atomic functions values; 3) procedure of verification has linear complexity in the number of values to be checked. Moreover, the algorithms proposed are implemented using Python programming language and a set of tables of atomic functions values are obtained. Conclusions: results of this research are expected to improve existing data processing technologies based on atomic functions, especially the algorithm DAC, and accelerate the development of new ones.

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Section: Dynamic Algorithm For Computation Of Atomic Functions Ups(x)mentioning

confidence: 91%

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of dynamic programming approach to computation of atomic functions

Makarichev

Kharchenko

2021

reks

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“…CSE is a compression algorithm for bit strings that was generalized to higher dimensions to handle all types of images. Makarichev et al [25] modified the irreversible discrete atomic compression (DAC) algorithm by adding compressed data describing the difference between the original image and the compressed one inside the corresponding DAC file. The addition combined with the compressed image results in a reconstructed image without any distortions.…”

Section: Related Workmentioning

confidence: 99%

An Improved Medical Image Compression Method Based on Wavelet Difference Reduction

et al. 2023

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Advanced microscopic techniques such as high-throughput, high-content, multispectral, and 3D imaging could include many images per experiment requiring hundreds of gigabytes (GBs) of memory. Efficient lossy image-compression methods such as joint photographic experts group (JPEG) and JPEG 2000 are crucial to managing these large amounts of data. However, these methods can get visual quality with high compression ratios but do not necessarily maintain the medical data and information integrity. This paper proposes a novel and improved medical image compression method based on color wavelet difference reduction. Specifically, the proposed method is an extension of the standard wavelet difference reduction (WDR) method using mean co-located pixel difference to select the optimum quantity of color images that present the highest similarity in the spatial and temporal domain. The images with large spatiotemporal coherence are encoded as one volume and evaluated regarding the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM). The proposed method is evaluated in the challenging histopathological microscopy image analysis field using 31 slides of colorectal cancer. It is found that the perceptual quality of the medical image is remarkably high. The results indicate that the PSNR improvement over existing schemes may reach up to 22.65 dB compared to JPEG 2000. Also, it can reach up to 10.33dB compared to a method utilizing discrete wavelet transform (DWT), leading us to implement a mobile and web platform that can be used for compressing and transmitting microscopic medical images in real time.

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Combined Lossless/Lossy Compression of Three-channel Images

Makarichev,

Lukin

2023

2023 13th International Conference on Dependable Systems, Services and Technologies (DESSERT)

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Lossless Discrete Atomic Compression of Full Color Digital Images

Cited by 7 publications

References 11 publications

Application of dynamic programming approach to computation of atomic functions

Application of dynamic programming approach to computation of atomic functions

An Improved Medical Image Compression Method Based on Wavelet Difference Reduction

Combined Lossless/Lossy Compression of Three-channel Images

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