Low-complexity Scaling Methods for DCT-II Approximations

TL;DR

This paper presents new low-complexity scaling methods for approximating DCT-II matrices, improving accuracy over existing methods and demonstrating practical hardware implementation advantages.

Contribution

The paper introduces novel scaling techniques based on Hou's recursive matrix factorization, outperforming the JAM scaling method in accuracy and efficiency.

Findings

Proposed scaling methods outperform JAM in total error energy.

Error analysis confirms good approximation quality.

Hardware implementation shows practical competitiveness.

Abstract

This paper introduces a collection of scaling methods for generating $2N$-point DCT-II approximations based on $N$-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $2N$-point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations that outperform the transforms resulting from the JAM scaling method according to total error energy and mean squared error. Orthogonality conditions are derived and an extensive error analysis based on statistical simulation demonstrates the good performance of the introduced scaling methods. A hardware implementation is also provided demonstrating the competitiveness of the proposed methods when compared to the JAM scaling method.