Enhancing an image’s compression while keeping quality standards utilizing new mathematical technology

Abstract

The rapid development of technology led to the need to keep pace with it, especially in the field of image processing, because of its importance in the need to get better results. In this paper, new discrete Chebyshev wavelet transforms (DChWT) derived from Chebyshev polynomials (ChP) were proposed and characterized. In terms of orthogonality and approximation (convergence) in the field of mathematics, (ChP) were qualified to transform into discrete wavelets called (DChWT), depending on the mother function with operators (s, r), and were used in image processing to analyze them in the low filter and the high filter so that the image is analyzed into coefficients. Proximity and detail coefficients, which lead to dividing the image into four parts, low left (LL), in which the proximity coefficients are concentrated while the rest of the parts are centered on the detail coefficients, which are high left (HL), low right (LR), and high right (HR), and image compression through the new filter, which has proven its efficiency at level (8) in our results. The results of the proposed wavelets in this work were reached in calculating quality standards in the image obtained after the compression process after comparing them with the results obtained using the standard wavelet used in HaarSymlet 2, Conflict 2, and Daubecheis 2. The most important of these standards is a mean square error (MSE), peak signal-to-noise ratio (PSNR), bit per pixel (BPP), compression ratio (CR), and table one. In this paper, the efficiency of the proposed new wavelets is explained after adding it to MATLAB and according to a specific program to drop in with the basic wavelets to take on their role in important tasks in the image processing area, like artificial intelligence