Regular Discrete Cosine Transform and its Application to Digital Images Representation

Abstract

Discrete cosine transform dct-i, unlike dct-ii, does not concentrate the energy of a transformed vector sufficiently well, so it is not used practically for the purposes of digital image compression. By performing regular normalization of the basic cosine transform matrix, we obtain a discrete cosine transform which has the same cosine basis as dct-i, coincides as dct-i with its own inverse transform, but unlike dct-i, it does not reduce the proper ability of cosine transform to the energy concentration. In this paper we consider briefly the properties of this transform, its possible integer implementation for the case of 8x8-matrix, its applications to the image itself and to the preliminary rgb colour space transformations, furthermore we investigate some models of quantization, perform an experiment for the estimation of the level of digital images compression and the quality achieved by use of this transform. This experiment shows that the transform can be sufficiently effective for practical use, but the question of its comparative effectiveness with respect to dct-ii remains open.