A Coordinate-based Fuzzy Encoding Strategy for Compressing Grayscale Images

<title>Abstract</title> Image compression techniques realized in various ways have become an indispensable part in the practical storage and transmission of digital images. In this study, we present a novel method of lossy compression based on sampling and fuzzy encoding for grayscale images and discuss the problem of their reconstruction. First, an image is divided into a number of non-overlapping blocks of pixels. Next, we perform multiple rounds of random sampling. In each round, a number of pixels are selected as prototypes for the representing the corresponding block. Each pixel in the block is reconstructed based on the gray-levels of the prototypes and membership degrees computed with respect to the distances of each pixel to the prototypes. The reconstruction abilities delivered by the prototypes are quantified by a certain objective fidelity criterion and the prototypes leading to lowest reconstruction error are determined as representatives of current block. Finally, once the representatives in each block have been determined, we reconstruct the whole image based on these prototypes. Experimental studies as well as visual evaluations show that the proposed algorithm is able to achieve high compression ratios while preserving the overall fidelity in the decompressed images.