### DISCRETE ATOMIC COMPRESSION OF DIGITAL IMAGES: ALMOST LOSSLESS COMPRESSION

#### Abstract

In this paper, we consider the problem of digital image compression with high requirements to the quality of the result. Obviously, lossless compression algorithms can be applied. Since lossy compression provides a higher compression ratio and, hence, higher memory savings than lossless compression, we propose to use lossy algorithms with settings that provide the smallest loss of quality. The **subject matter** of this paper is almost lossless compression of full color 24-bit digital images using the discrete atomic compression (DAC) that is an algorithm based on the discrete atomic transform. The **goal** is to investigate the compression ratio and the quality loss indicators such as uniform (U), root mean square (RMS) and peak signal to noise ratio (PSNR) metrics. We also study the distribution of the difference between pixels of the original image and the corresponding pixels of the reconstructed image. In this research, the classic test images and the classic aerial images are considered. U-metric, which is highly dependent on even minor local changes, is considered as the major metric of quality loss. We solve the following **tasks**: to evaluate memory savings and loss of quality for each test image. We use the **methods** of digital image processing, atomic function theory, and approximation theory. The computer program "Discrete Atomic Compression: User Kit" with the mode "Almost Lossless Compression" is used to obtain results of the DAC processing of test images. We obtain the following **results**: 1) the difference between the smallest and the largest loss of quality is minor; 2) loss of quality is quite stable and predictable; 3) the compression ratio depends on the smoothness of the color change (the smallest and the largest values are obtained when processing the test images with the largest and the smallest number of small details in the image, respectively); 4) DAC provides 59 percent of memory savings; 5) ZIP-compression of DAC-files, which contain images compressed by DAC, is efficient. **Conclusions:** 1) the almost lossless compression mode of DAC provides sufficiently stable values of the considered quality loss metrics; 2) DAC provides relatively high compression ratio; 3) there is a possibility of further optimization of the DAC algorithm; 4) further research and development of this algorithm are promising.

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DOI: https://doi.org/10.32620/reks.2019.1.03

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