Lossless Compression of Grayscale and Colour Images Using Multidimensional CSE

Abstract

Originally, compression by substring enumeration (CSE) is a lossless compression technique that is intended for strings of bits. As such, the original version is one-dimensional. An extension of CSE for strings drawn from a larger alphabet has later been introduced. Also, CSE has recently been extended to two-dimensional (2D) data. As such, 2D CSE can be used directly to compress images. Unfortunately, CSE generally does not perform on data drawn from large alphabets as well as on binary data. This means that, although we can expect 2D CSE to perform well on bilevel images, we must expect a loss of performance on grayscale and colour images, where the alphabet sizes may be 28 and 224, respectively, as in common image formats. As a workaround for this difficulty, we propose to handle grayscale and colour images by remaining in the realm of binary data but by extending CSE to higher dimensions. Grayscale images may have the levels of gray of their pixels decomposed into bit planes and, then, get compressed using a 3D CSE. Colour images may have their three colour channels treated as yet another dimension and, then, get compressed using a 4D CSE. Actual empirical measurements are deferred to another paper as we do not have a working implementation of multidimensional CSE yet.