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Integer DCT Approximation With Arbitrary Size and Adjustable Precision

Thomaz, L. A. ; Assunção, P.A. ; Távora, L. ; Faria, S.M.M.

IEEE Signal Processing Letters Vol. 27, Nº -, pp. 965 - 969, May, 2020.

ISSN (print): 1070-9908
ISSN (online): 1558-2361

Journal Impact Factor: 1,751 (in 2014)

Digital Object Identifier: 10.1109/lsp.2020.2998362

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Abstract
This letter proposes a method to obtain integer reversible discrete cosine transforms for generic transform-based coding schemes. The novelty of the proposed method, which is based on decomposition of the DCT-II matrix into two triangular and one diagonal matrices, is twofold: (i) the new matrices can be of arbitrary size, i.e., any square N×N dimension, thus suitable for applications where non power-of-2 dimensions are required; (ii) they can be designed with adjustable precision in a trade-off with the number of representation bits. Furthermore, improvements are also proposed over the base scheme to avoid numerical issues when working with large matrices and to obtain more reliable approximations. The performance evaluation demonstrate the effectiveness of the proposed transforms to approximate the coding gain capabilities of the original DCT-II.