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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (8): 58-64.doi: 10.6040/j.issn.1671-9352.0.2016.474

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A分级硬阈值追踪

施章磊,李维国   

  1. 中国石油大学(华东)理学院, 山东 青岛 266580
  • 收稿日期:2016-10-13 出版日期:2017-08-20 发布日期:2017-08-03
  • 作者简介:施章磊(1991— ),男,硕士研究生,研究方向为信号与图形处理. E-mail:shizhanglei2010@163.com
  • 基金资助:
    中央高校基本科研基金资助项目(15CX08011A);国家自然科学基金资助项目(60971132)

A graded hard thresholding pursuit algorithm

SHI Zhang-lei, LI Wei-guo   

  1. College of Science, China University of Petroleum, Qingdao 266580, Shandong, China
  • Received:2016-10-13 Online:2017-08-20 Published:2017-08-03

摘要: 受到硬阈值追踪算法(HTP)的启发,提出了用于求解压缩感知问题的A硬阈值追踪算法(A graded hard thresholding pursuit algorithm, APGHTP), 并在约束等距条件下给出了该算法的理论保证。在数值实验中,不论测量值是否包含误差, APGHTP都表现较好,证明了该算法的稀疏恢复能力。在恢复稀疏向量时, APGHTP所需的迭代数与稀疏向量的稀疏度相同。

关键词: 稀疏解, Moore-Penrose逆, 压缩感知, 硬阈值追踪

Abstract: Inspired by hard thresholding pursuit algorithm(HTP). A graded hard thresholding pursuit algorithm(APGHTP)was proposed for solving compressive sensing problems. The theoretical guarantees of the new algorithm were given under restricted isometry property(RIP)condition.In the numerical experiment, regardless of whether the measured value contains error, APGHTP performance is better, which proves the sparse recovery ability of the algorithm.When recovering sparse vectors, the number of iterations required for APGHTP is the same as that of sparse vectors.

Key words: hard thresholding pursuit, Moore-Penrose inverse, compressive sensing, sparse solution

中图分类号: 

  • O242
[1] NATARAJAN B K. Sparse approximate solutions to linear systerms[J]. SIAM Journal on Computing, 1995, 24(2):227-234.
[2] CANDÈS E J, ROMBERG J K, TAO TERENCE. Stable signal recovery from incomplete and inaccurate measurements[J].Communications on Pure & Applied Mathematics, 2005, 59(8):410-412.
[3] DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[4] DONOHO D L. Neighborly polytopes and sparse solution of underdetermined linear equations[EB/OL].[2016-04-06]. http://statweb.stanford.edu/~donoho/Reports/2005/NPa SSULE-01-28-05.pdf
[5] DONOHO D L. High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension[J]. Discrete & Computational Geometry, 2006, 35(4):617-652.
[6] TROPP J A, GILBERT A C. Signal recovery from random measurements via orthogonal matching pursuit[J]. IEEE Transactions on Information Theory, 2007, 53(12):4655-4666.
[7] NEEDELL D, TROPP J A. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples[J]. Applied & Computational Harmonic Analysis, 2008, 26(3):301-321.
[8] BLUMENSATH T, DAVIES M E. Iterative hard thresholding for compressed sensing[J]. Applied & Computational Harmonic Analysis, 2009, 27(3):265-274.
[9] DONOHO D L. De-noising by soft-thresholding[J]. IEEE Transactions on Information Theory, 1995, 41(3):613-627.
[10] YIN Wotao, OSHER S, GOLDFARB D, et al. Bregman iterative algorithms for l1-minimization with applications to compressed sensing[J]. Siam Journal on Imaging Sciences, 2008, 1(1):143-168.
[11] YIN Wotao. Analysis and generalizations of the linearized bregman method[J].Siam Journal on Imaging Sciences, 2010, 3(4):856-877.
[12] FOUCART S. Hard thresholding pursuit: an algorithm for compressive sensing[J]. Siam Journal on Numerical Analysis, 2011, 49(6):2543-2563.
[13] BOUCHOT J L, FOUCART S, HITCZENKO P. Hard thresholding pursuit algorithms: number of iterations[J]. Applied & Computational Harmonic Analysis, 2016, 41(2):412-435.
[14] BEN-ISRAEL A, GREVILLE T N E. Generalized inverses[M].New York: Springer-Verlag, 2003.
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