一种采用矩阵分解的正交4抽头多小波无损压缩算法

景明利 1; 2; 齐春 1

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一种采用矩阵分解的正交4抽头多小波无损压缩算法

更新时间：2025-07-09

- 一种采用矩阵分解的正交4抽头多小波无损压缩算法
- Orthogonal 4-Tap Multiwavelet Transform for Lossless Compression
- 西安交通大学学报 2011年45卷第2期页码：54-58
- 作者机构：
  
  1. 西安交通大学电子与信息工程学院,西安,710049
  2. 西安财经学院统计学院,西安,710100
- 作者简介：
- 基金信息：
  
  :2010-05-19. 作者简介: 景明利(1977-),男,博士生;齐春(联系人),男,教授,博士生导师. 基金项目:国家自然科学基金资助项目(60972124);国家“863计划”资助项目(2009AA01Z321)
- DOI：
  中图分类号： TN911
- 网络首发：2011-02-10，
  
  纸质出版：2011
- 稿件说明：
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景明利 1, 2, 齐春 1. 一种采用矩阵分解的正交4抽头多小波无损压缩算法[J]. 西安交通大学学报, 2011,45(2):54-58.

Orthogonal 4-Tap Multiwavelet Transform for Lossless Compression[J]. 2011, 45(2): 54-58.
景明利 1, 2, 齐春 1. 一种采用矩阵分解的正交4抽头多小波无损压缩算法[J]. 西安交通大学学报, 2011,45(2):54-58. DOI：

Orthogonal 4-Tap Multiwavelet Transform for Lossless Compression[J]. 2011, 45(2): 54-58. DOI：

摘要

针对4抽头多小波整数变换算法在图像无损压缩中加权熵较大的问题

提出了一种利用矩阵奇异值分解和三角分解的4抽头正交多小波整数变换算法.首先把多小波系数矩阵组成的右循环变换矩阵分解为两个块对角阵与一个置换阵之积

并对块对角阵中的块矩阵进行基本三角分解

其次对输入图像中的每一列依次与基本三角阵相乘

并对每一次相乘的结果进行取整运算

最后在输入图像列变换结果的基础上对每一行再重复上述对图像的列运算.因为在整个变换过程中该算法实现了原位计算

所以减少了运算的存储空间和运算时间.对CL、DGHM、SA4、SA4-1、SA4-2、SA4-3、OPTFR多小波的实验结果表明:相对于4抽头多小波Van Fleet 算法

该算法对图像压缩的加权熵减少了1.9～2.8 b.

Abstract

An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. By the singular value decomposition(SVD)

the transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix

and the block matrix in block diagonal matrices is factorized into triangular elementary reversible matrices(TERMs)

which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increasing dimension of transform matrix

and the proposed algorithm is in-place calculation without allocating auxiliary memory. The examples of integer multiwavelet transform for CL

DGHM

SA4

SA4-1

SA4-2

SA4-3 and OPTFR verify that the proposed algorithm outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform. Compared with the Van Fleet algorithm

the weighted entropy of the proposed method is decreased by 1.9-2.8 bits.

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Keywords

references

CALDERBANK A R, DAUBECHIES I, SWELDENS W, et al. Wavelet transforms that map integers to integers[J]. Applied and Computational Harmonic Analysis,1998, 5(3): 332-369.

DEEVER A T, HEMAMI S S. Lossless image compression with projection-based and adaptive reversible integer wavelet transforms[J]. IEEE Transactions on Image Processing, 2003, 12(5):489-499.

COTRONEI M, MONTEFUSCO L B, PUCCIO L. Multiwavelet analysis and signal processing[J]. IEEE Transactions on Circuits and Systems,1998, 45(8):970-987.

STRELA V, HELLER P N, STRANG G, et al. The application of multiwavelet filterbanks to image processing[J]. IEEE Transactions on Image Processing, 1999, 8(4): 548-563.

XIA X G. A new prefilter design for discrete multiwavelet transforms[J]. IEEE Transactions on Signal Processing, 1998, 46(6): 1558-1570.

CHEUNG K W, PO L M. Integer multiwavelet transform for lossless image coding[C]∥Proceedings of 2001 International Symposium on Intelligent Multimedia Video and Speech Processing. Piscataway,NJ,USA: IEEE, 2001:117-120.

HUANG B, SRIRAJA Y, HUANG H L, et al. Lossless multiwavelet compression of ultraspectral sounder data[C]∥IEEE International Conference on Geoscience and Remote Sensing Symposium. Piscataway, NJ, USA: IEEE, 2006:3541-3544.

VAN FLEET P J. Multiwavelets and integer transforms[J]. Journal of Computational Analysis and Applications,2003,5(1):161-178.

JING Mingli, HUANG Hua, LIU Wuling, et al. A general approach for orthogonal 4-tap integer multiwavelet transforms[J]. Mathematical Problems in Engineering, 2010,2010:1-12.

HAO Pengwei, SHI Qinyun. Matrix factorizations for reversible integer mapping[J]. IEEE Transactions on Signal Processing, 2001,49(10):2314-2324.

DONOVAN G, GERONIMO J S, HARDIN D, et al. Construction of orthogonal wavelets using fractal interpolation function[J]. SIAM J Math Anal, 1996,27(4): 1158-1192.

CHUI C K, LIAN J A. A study of orthonormal multiwavelets[J]. Applied Numerical Mathematics, 1996, 20(3):273-298.

THAM J Y, SHEN L, LEE S L, et al. A general approach for analysis and application of discrete multiwavelet transforms[J]. IEEE Transactions on Signal Processing, 2000, 48(2):457-464.

THAM J Y, SHEN L, LEE S L, et al. A new multifilter design property for multiwavelet image compression[C]∥IEEE International Conference on Acoustics, Speech, and Signal Processing. Piscataway, NJ, USA: IEEE, 1999:1229-1232.

JIANG Q T. On the design of multifilter banks and orthonormal multiwavelet bases[J]. IEEE Transactions on Signal Processing, 1998, 46(12):3292-3303.

ATTATITMONGCOL K, HARDIN D P,WILKES D M. Multiwavelet prefilters: part II optimal orthogonal prefilters[J]. IEEE Transactions on Image Processing, 2001, 10(10):1476-1487.

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