Approximate calculation of 8-point DCT for various scenarios of practical applications

Abstract

In this paper, based on the parametric model of the matrix of discrete cosine transform (DCT), and using an exhaustive search of the parameters’ space, we seek for the best approximations of 8-point DCT at the given computational complexities by taking into account three different scenarios of practical usage. The possible parameter values are selected in such a way that the resulting transforms are only multiplierless approximations, i.e., only additions and bit-shift operations are required. The considered usage scenarios include such cases where approximation of DCT is used: (i) at the data compression stage, (ii) at the decompression stage, and (iii) both at the compression and decompression stages. The obtained results in effectiveness of generated approximations are compared with results of popular known approximations of 8-point DCT of the same class (i.e., multiplierless approximations). In addition, we perform a series of experiments in lossy compression of natural images using popular JPEG standard. The obtained results are presented and discussed. It should be noted, that in the overwhelming number of cases the generated approximations are better than the known ones, e.g., in asymmetric scenarios even by more than 3 dB starting from entropy of 2 bits per pixel. In the last part of the paper, we investigate the possibility of hardware implementation of generated approximations in Field-Programmable Gate Array (FPGA) circuits. The results in the form of resource and energy consumption are presented and commented. The experiment outcomes confirm the assumption that the considered class of transformations is characterized by low resource utilization.