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Integer DCT Approximation with Arbitrary Size and Adjustable Precision
IEEE Signal Processing Letters ( IF 3.9 ) Pub Date : 2020-01-01 , DOI: 10.1109/lsp.2020.2998362
Lucas A. Thomaz , Pedro A. A. Assuncao , Luis M. N. Tavora , Sergio M. M. de Faria

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 $N\times N$ 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.

中文翻译:

具有任意大小和可调精度的整数 DCT 近似

这封信提出了一种为通用的基于变换的编码方案获得整数可逆离散余弦变换的方法。所提出的方法基于将 DCT-II 矩阵分解为两个三角形矩阵和一个对角矩阵,其新颖性是双重的:(i) 新矩阵可以是任意大小,即任何正方形 $N\times N $ 维度,因此适用于需要非 2 次幂维度的应用;(ii) 它们可以在与表示位数的权衡中以可调精度设计。此外,还提出了对基本方案的改进,以避免在处理大型矩阵时出现数值问题并获得更可靠的近似值。
更新日期:2020-01-01
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