计算机科学 ›› 2013, Vol. 40 ›› Issue (Z6): 93-95.

• 智能算法与优化 • 上一篇    下一篇

一种求解稀疏信号重构的新算法

戚平   

  1. 中国石油大学华东计算机与通信工程学院 青岛266580
  • 出版日期:2018-11-16 发布日期:2018-11-16

New Algorithm for Sparse Signals Reconstruction

QI Ping   

  • Online:2018-11-16 Published:2018-11-16

摘要: 由于允许从少量数据中恢复原始信号的压缩感知的引入,基于1范数正则化的最优化方法近来越来越受到重视。利用最小二乘问题的一种等价形式和Bregman迭代方法的一些技巧,本文推导出了可以用于稀疏信号重构求解的非满秩情况下的A+线性Bregman迭代方法的一种新的等价形式,并证明了它与原形式的等价性。

关键词: 最小二乘问题,Bregman迭代正则化,Moore-Penrose逆

Abstract: The class of 1 norm regularization problems has received much attention recently because of the introduction of “compressed sensing” which allows signals to be reconstructed from small amounts of data.With an equivalent form of least squares problem and some techniques of Bregman iterative methods,we induced a derivation of A+ linear Bregman iteration method that is equivalent to the one that exits.

Key words: Least squares problem,Bregman iterative regularization,Moore-Penrose inverse

[1] Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].SIAM J.Sci.Comput,1998,20:33-61
[2] Candes E,Romberg J,Tao T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J].IEEE Trans.Inform.Theory,2006,52:489-509
[3] Donoho D L.Compressed Sensing[J].IEEE Trans.Inform.Theory,2006,52:1289-1306
[4] Hale E,Yin W,Zhang Y.A Fixed-Point Continuation Method for L1-Regularization with Application to Compressed Sensing[R].CAAM Technical Report tr07-07.Rice University,Houston,TX,2007
[5] Yin W,Osher S,Goldfarb D,et al.Bregman iterative algorithms for 1-Regularization with Application to Compressed Sensing [J].SIAM J.Imaging Sciences, 2008,1:143-168
[6] Cai J F,Chan R H,Shen Z.Linearizad Bregman iterations forcompresses sensing[J].Math.Comp.,2009,78(267):1515-1536
[7] Cai J F,Osher S,Shen S W.Linearized Bregman Iteration for Frame-Based Image Deblurring[J].SIAM J.Imaging Sciences,2009,2(1):226-252
[8] 张慧,成礼智.A-线性Bregman迭代算法[J].计算数学,2010,32(1):97-104
[9] Ben-Israel A,Greville T N E.Generalized inverses:Theory and Applications(2nd ed)[M].New York,NY:Springer,2003:35-130
[10] Osher S,Mao Y,Dong B,et al.Fast Linearized Bregman Iteration for Compressed Sensing and Sparse Denoising[R].Report 08-37,UCLA.CAM,2008:1-18
[11] Donoho D L.Denoising by softthresholding[J].IEEE Trans.Inform.Theory,1995,3:613-627

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!