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Keywords

Discrete Cosine Transform; Sparse and Orthogonal Factors; Radix-2 Algorithms; Recursive Algorithms; Stable Algorithms; Arithmetic Cost; Error Bounds; Image Reconstruction; Signal Flow Graphs.

Abstract

This paper presents stable, radix-2, completely recursive discrete cosine transform 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. Signal flow graphs are demonstrated based on the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having orthogonal factors. Finally image compression results are presented based on the recursive 2D DCT-II and DCT-IV algorithms for image size 512 by 512 pixels with transfer block sizes 8 by 8, 16 by 16, and 32 by 32 with 93.75% absence of coefficients in each transfer block.

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