A low multiplicative complexity fast recursive DCT-2 algorithm

Abstract

A fast Discrete Cosine Transform (DCT) algorithm is introduced that can be of particular interest in image processing. The main features of the algorithm are regularity of the graph and very low arithmetic complexity. The 16-point version of the algorithm requires only 32 multiplications and 81 additions. The computational core of the algorithm consists of only 17 nontrivial multiplications, the rest 15 are scaling factors that can be compensated in the post-processing. The derivation of the algorithm is based on the algebraic signal processing theory (ASP). MATLAB implementation of the algorithm can be found in the public repository https://github.com/Mak-Sim/Fast_recursive_DCT.