带有噪音的稀疏解的稳定性分析的注

doi:10.6040/j.issn.1672-3961.0.2015.032

山东大学学报(工学版) ›› 2015, Vol. 45 ›› Issue (4): 91-94.doi: 10.6040/j.issn.1672-3961.0.2015.032

• 信息科学与工程 • 上一篇

带有噪音的稀疏解的稳定性分析的注

崔安刚, 李海洋, 任璐

西安工程大学理学院, 陕西西安 710048

收稿日期:2015-02-08 修回日期:2015-05-26 出版日期:2015-08-20 发布日期:2015-02-08
通讯作者: 李海洋(1975-),男,陕西富平人,教授,博士,主要研究方向为稀疏信息处理,量子逻辑,格上拓扑学等.E-mail:fplihaiyang@126.com E-mail:fplihaiyang@126.com
作者简介:崔安刚(1989-),男,山东临沂人,主要硕士研究生,研究方向为稀疏信息处理.E-mail:cuiangang@163.com
基金资助:
国家自然科学基金资助项目(11271297);陕西省教育厅专项科研计划项目资助项目(14JK1299);西安工程大学研究生创新基金资助项目(CX2015012)

A note on the analysis of stability of noised sparse solutions

CUI Angang, LI Haiyang, REN Lu

School of Science, Xi'an Polytechnic University, Xi'an 710048, Shaanxi, China

Received:2015-02-08 Revised:2015-05-26 Online:2015-08-20 Published:2015-02-08

摘要/Abstract

摘要： DONOHO D L, ELAD M等人分别利用矩阵的相干性和spark_η(A)的性质证明了(P₀^ε)问题的稳定性定理。本研究首先通过反例指出ELAD M的证明过程存在错误,其次利用spark_η(A)和矩阵奇异值的性质重新证明(P₀^ε)问题的稳定性定理。

关键词: 噪音, 矩阵奇异值, 稳定性, 欠定线性方程组, 稀疏解

Abstract: Donoho D L and Elad M proved stability theorem of problem (P₀^ε) by using the properties of matrix's mutual-coherence and spark_η(A) respectively. Counter-example was used to show that there were some mistakes in Elad M's proof, and then stability theorem of problem (P₀^ε) was reproved by using the properties of spark_η(A) and the singular value of matrix.

Key words: the underdetermined linear systems, singular value of matrix, stability, sparse solution, noise

中图分类号:

O242.2

崔安刚, 李海洋, 任璐. 带有噪音的稀疏解的稳定性分析的注[J]. 山东大学学报(工学版), 2015, 45(4): 91-94.

CUI Angang, LI Haiyang, REN Lu. A note on the analysis of stability of noised sparse solutions[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2015, 45(4): 91-94.

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带有噪音的稀疏解的稳定性分析的注

A note on the analysis of stability of noised sparse solutions

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