Discrete Atomic Compression of Digital Images

Abstract

The subject matter of this paper is the discrete atomic compression (DAC) of digital images, which is a lossy compression process based on the discrete atomic transform (DAT). The goal is to investigate the efficiency of the DAC algorithm. We solve the following tasks: to develop a general compression scheme using discrete atomic transform and to compare the results of DAC and JPEG algorithms. In this article, we use the methods of digital image processing, atomic function theory, and approximation theory. To compare the efficiency of DAC with the JPEG compression algorithm we use the sets of the classic test images and the classic aerial images. We analyze compression ratio (CR) and loss of quality, using uniform (U), root mean square (RMS) and peak signal to noise ratio (PSNR) metrics. DAC is an algorithm with flexible parameters. In this paper, we use “Optimal” and “Allowable” modes of this algorithm and compare them with the corresponding modes of JPEG. We obtain the following results: 1) DAC is much better than JPEG by the U-criterion of quality loss; 2) there are no significant differences between DAC and JPEG by RMS and PSNR criterions; 3) the compression ratio of DAC is much higher than the compression ratio of JPEG. In other words, the DAC algorithm saves more memory than the JPEG compression algorithm with not worse quality results. These results are due to the fundamental properties of atomic functions such as good approximation properties, the high order of smoothness and existence of locally supported basis in the spaces of atomic functions. Since generalized Fup-functions have the same convenient properties, it is clear that such compression results can be achieved by application of a generalized discrete atomic transform, which is based on these functions. We also discuss the obtained results in the terms of approximation theory and function theory. Conclusions: 1) it is possible to achieve better results with DAC than with JPEG; 2) application of DAC to image compression is more preferable than JPEG in the case when it is planned to use recognition algorithms; 3) further development and investigation of the DAC algorithm are promising