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  1. (西安电子科技大学 电子工程学院,陕西 西安 710071)
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2008-04-20 发布日期:2008-03-28
  • 通讯作者: 刘丹华

New method for signal sparse decomposition over a redundant dictionary

LIU Dan-hua;SHI Guang-ming;ZHOU Jia-she

  1. (School of Electronic Engineering, Xidian Univ., Xi′an 710071, China)
  • Received:1900-01-01 Revised:1900-01-01 Online:2008-04-20 Published:2008-03-28
  • Contact: LIU Dan-hua

摘要: 针对目前冗余字典下信号稀疏分解常用算法计算复杂度高的问题,提出一种分组匹配追踪算法.该算法首先利用多组正交基构造冗余字典,然后采用迭代式分组匹配追踪,每次迭代从字典中选出一组和原始信号或残余最匹配的正交基,采用正交分解快速算法进行正交分解得到少量重要系数,多次迭代后逐渐稀疏逼近原始信号.实验结果表明,基于小波正交基级联冗余字典进行信号稀疏分解时,在同等稀疏条件下,与匹配追踪(MP)算法相比,该算法的计算速度提高了大约30倍,而且可避免过匹配现象.

关键词: 稀疏分解, 冗余字典, 匹配追踪算法, 信号压缩

Abstract: For the extremely high complexity of usual algorithms for sparse decomposition, a new group matching pursuit algorithm is presented based on a redundant dictionary with several orthonormal bases. The algorithm adopts the the idea of iterative group matching pursuit and selects the optimal basis from the dictionary by comparing the matching degree between the signal or the residua and every basis. Each operation of decomposing results in a few important coefficients by using the fast calculating algorithm of orthogonal decomposition. After several such iterations, the original signal is approximated with a few coefficients eventually. Simulation results show that the calculating speed of the algorithm in this paper increases by about thirty times compared with MP’s. Moreover, this algorithm can avoid over-matching.

Key words: sparse decomposition, redundant dictionary, matching pursuit algorithm, signal compression


  • TN911.72