A low multiplicative complexity fast recursive DCT-2 algorithm

TL;DR

This paper presents a novel 16-point recursive DCT-2 algorithm with low multiplicative complexity, regular structure, and efficient computation, suitable for image processing applications.

Contribution

It introduces a new recursive DCT-2 algorithm based on algebraic signal processing theory with significantly reduced multiplications and a regular graph structure.

Findings

Requires only 32 multiplications and 81 additions for 16-point DCT

Contains only 17 nontrivial multiplications in the core

Implementation available in MATLAB repository

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.