钟轶群,李崇君.利用分片贪婪算法求解分片稀疏恢复问题[J].数学研究及应用,2018,38(6):643~658
利用分片贪婪算法求解分片稀疏恢复问题
Piecewise Sparse Recovery via Piecewise Greedy Method
投稿时间:2018-06-07  修订日期:2018-09-14
DOI:10.3770/j.issn:2095-2651.2018.06.010
中文关键词:  分片稀疏  正交匹配追踪算法(OMP)  贪婪算法
英文关键词:piecewise sparse  OMP  greedy algorithms
基金项目:国家自然科学基金 (Grant Nos.11471066; 11572081; 11871137), 中央高校研究基金 (Grant No.QYWKC2018007).
作者单位
钟轶群 大连理工大学数学科学学院, 辽宁 大连 116024 
李崇君 大连理工大学数学科学学院, 辽宁 大连 116024 
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中文摘要:
      在实际应用中,有一些信号是具有分片的结构的.本文我们提出一种分片正交匹配追踪算法(P\_OMP)来求解分片稀疏恢复问题,旨在保护分片信号中的分片结构(或者小尺度非零元).P\_OMP算法是基于CoSaMP和OMMP算法的思想上延伸出的一种针对分片稀疏问题的贪婪算法. P\_OMP算法不仅仅具有OMP算法的优势,还能够在比CoSaMP方法更松弛的条件下得到同样的误差下降速率.进一步,P\_OMP~算法在保护分片稀疏信号的尺度细节信息上表现的更好.数值实验表明相比于CoSaMP, OMP, OMMP和BP算法, P\_OMP算法在分片稀疏恢复上更有效更稳定.
英文摘要:
      In some applications, there are signals with piecewise structure to be recovered. In this paper, we propose a piecewise OMP (P\_OMP) method which aims to preserve the piecewise sparse structure (or the small-scaled entries) of piecewise signals. Besides the merits of OMP, the P\_OMP, which is a generalization of the combination of CoSaMP and OMMP (Orthogonal Multi-matching Pursuit) on piecewise sparse recovery, possesses the advantages of comparable approximation error decay as CoSaMP with more relaxed sufficient condition and better recovery success rate. Moreover, the P\_OMP algorithm recovers the piecewise sparse signal according to its piecewise structure, which results in better details preservation. Numerical experiments indicate that compared with CoSaMP, OMP, OMMP and BP methods, the P\_OMP algorithm is more effective and robust for piecewise sparse recovery.
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