| 带有噪音的稀疏解的稳定性分析的注 |
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| 引用本文： | 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. DOI: 10.6040/j.issn.1672-3961.0.2015.032 |
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| 作者姓名： | 崔安刚 李海洋 任璐 |
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| 作者单位： | 西安工程大学理学院, 陕西 西安 710048 |
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| 基金项目： | 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) |
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| 摘 要： | DONOHO D L, ELAD M等人分别利用矩阵的相干性和sparkη(A)的性质证明了(P0ε)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sparkη(A)和矩阵奇异值的性质重新证明(P0ε)问题的稳定性定理。
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| 关 键 词： | 噪音 矩阵奇异值 稳定性 欠定线性方程组 稀疏解 |
| 收稿时间： | 2015-02-08 |
A note on the analysis of stability of noised sparse solutions |
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| CUI Angang,LI Haiyang,REN Lu. A note on the analysis of stability of noised sparse solutions[J]. Journal of Shandong University of Technology, 2015, 45(4): 91-94. DOI: 10.6040/j.issn.1672-3961.0.2015.032 |
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| Authors: | CUI Angang LI Haiyang REN Lu |
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| Affiliation: | School of Science, Xi'an Polytechnic University, Xi'an 710048, Shaanxi, China |
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| Abstract: | Donoho D L and Elad M proved stability theorem of problem (P0ε) by using the properties of matrix's mutual-coherence and sparkη(A) respectively. Counter-example was used to show that there were some mistakes in Elad M's proof, and then stability theorem of problem (P0ε) was reproved by using the properties of sparkη(A) and the singular value of matrix. |
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| Keywords: | the underdetermined linear systems singular value of matrix stability sparse solution noise |
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