Signal Processing based on Stable radix-2 DCT Algorithms having Orthogonal Factors

TL;DR

This paper introduces stable, recursive radix-2 DCT algorithms with orthogonal factors, providing error bounds and demonstrating their application in image compression and signal flow graph design.

Contribution

It presents new recursive DCT algorithms based on orthogonal, sparse factors, with error analysis and practical image compression results.

Findings

Error bounds for recursive DCT algorithms established

Effective image compression with high coefficient sparsity

Signal flow graphs demonstrated for recursive DCTs

Abstract

This paper presents stable, radix-2, completely recursive discrete cosine transformation algorithms DCT-I and DCT-III solely based on DCT-I, DCT-II, DCT-III, and DCT-IV having sparse and orthogonal factors. Error bounds for computing the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having sparse and orthogonal factors are addressed. Image compression results are presented based on the recursive 2D DCT-II and DCT-IV algorithms for image size $512 \times 512$ pixels with transfer block sizes $8 \times 8$, $16 \times 16$, and $32 \times 32$ with $93.75\%$ absence of coefficients in each transfer block. Finally signal flow graphs are demonstrated based on the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having orthogonal factors.