正交U变换及其快速算法

郭芬红; 熊昌镇

doi:10.11834/jig.20110825

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专辑

正交U变换及其快速算法
Orthogonal U transform and its fast algorithm
2011年16卷第8期页码：1552-1560
网络出版：2011-08-22，

纸质出版：2011
DOI： 10.11834/jig.20110825
稿件说明：

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郭芬红, 熊昌镇. 正交U变换及其快速算法[J]. 中国图象图形学报, 2011,16(8):1552-1560. DOI： 10.11834/jig.20110825.

Orthogonal U transform and its fast algorithm[J]. Journal of Image and Graphics, 2011, 16(8): 1552-1560. DOI： 10.11834/jig.20110825.

摘要

采用递推方法构造一种正交变换，称之为U变换，该变换含有分段常数基向量、分段一次多项式基向量以及分段二次多项式基向量，是对Walsh变换、斜变换的推广。根据递推方式，可以得到相应的快速算法。利用平移复制算子和Kronecher积的性质，推导基于Kronecher积的快速算法和正交U变换的直接分解算法。将该变换应用于图像压缩中，构造基于人类视觉系统的量化表，实验结果表明，正交U变换的图像压缩性能明显优于斜变换的图像压缩性能，与DCT变换的图像压缩性能相当，为图像压缩提供了一种新的选择。

Abstract

In this paper

a new unitary transform called U transform is constructed with the recursion method.The U transform contains piecewise constant basis vectors

piecewise linear basis vectors and piecewise polynomials of degree 2 basis vectors

and so it is a generalization of Walsh transform and Slant transformThe corresponding fast algorithm based on Kronecher product is deduced.The new orthogonal U transform is applied to digital image compression with quantization table based on Human Visual System(HVS).The experimental results indicate that the compression performance of U transform outperforms the Slant transform and is equivalent to that of DCT.