A Class of DCT Approximations Based on the Feig-Winograd Algorithm

TL;DR

This paper introduces a new class of DCT approximations derived from the Feig-Winograd algorithm, optimizing for low complexity, near orthogonality, and high performance in image compression tasks.

Contribution

It proposes a unified parametrization of DCT approximations, leading to novel solutions optimized via multicriteria methods for improved efficiency and performance.

Findings

New DCT approximations outperform existing methods in proximity and coding performance.

Proposed methods exhibit low computational complexity and near orthogonality.

Some solutions achieve Pareto efficiency in the trade-off between complexity and accuracy.

Abstract

A new class of matrices based on a parametrization of the Feig-Winograd factorization of 8-point DCT is proposed. Such parametrization induces a matrix subspace, which unifies a number of existing methods for DCT approximation. By solving a comprehensive multicriteria optimization problem, we identified several new DCT approximations. Obtained solutions were sought to possess the following properties: (i) low multiplierless computational complexity, (ii) orthogonality or near orthogonality, (iii) low complexity invertibility, and (iv) close proximity and performance to the exact DCT. Proposed approximations were submitted to assessment in terms of proximity to the DCT, coding performance, and suitability for image compression. Considering Pareto efficiency, particular new proposed approximations could outperform various existing methods archived in literature.