ON ESTIMATES OF COEFFICIENTS OF GENERALIZED ATOMIC WAVELETS EXPANSIONS AND THEIR APPLICATION TO DATA PROCESSING

• Main Authors: Victor Olexandrovych Makarichev, Vladimir Vasilyevich Lukin, Iryna Victorivna Brysina
• Format: Article
• Language: English
• Published: National Aerospace University «Kharkiv Aviation Institute» 2020-01-01
• Series: Радіоелектронні і комп'ютерні системи
• Subjects: lossy image compression; discrete atomic compression; generalized atomic wavelets; maximum absolute deviation; quality loss control
• Online Access: http://nti.khai.edu/ojs/index.php/reks/article/view/1084

Discrete atomic compression (DAC) of digital images is considered. It is a lossy compression algorithm. The aim of this paper is to obtain a mechanism for control of quality loss. Among a large number of different metrics, which are used to assess loss of quality, the maximum absolute deviation or the MAD-metric is chosen, since it is the most sensitive to any even the most minor changes of processed data. In DAC, the main loss of quality is got in the process of quantizing atomic wavelet coefficients that is the subject matter of this paper. The goal is to investigate the effect of the quantization procedure on atomic wavelet coefficients. We solve the following task: to obtain estimates of these coefficients. In the current research, we use the methods of atomic function theory and digital image processing. Using the properties of the generalized atomic wavelets, we get  estimates of generalized atomic wavelet expansion coefficients. These inequalities provide dependence of quality loss measured by the MAD-metric on the parameters of quantization in the form of upper bounds. They are confirmed by the DAC-processing of the test images. Also, loss of quality measured by root mean square (RMS) and peak signal to noise ratio (PSNR) is computed. Analyzing the results of experiments, which are carried out using the computer program "Discrete Atomic Compression: Research Kit", we obtain the following results: 1) the deviation of the expected value of MAD from its real value in some cases is large; 2) accuracy of the estimates depends on parameters of quantization, as well as depth of atomic wavelet expansion and type of the digital image (full color or grayscale); 3) discrepancies can be reduced by applying a correction coefficient; 4) the ratio of the expected value of MAD to its real value behaves relatively constant and the ratio of the expected value of MAD to RMS and PSNR do not. Conclusions: discrete atomic compression of digital images in combination with the proposed method of quality loss control provide obtaining results of the desired quality and its further development, research and application are promising.