Signal recovery under mutual incoherence property and oracle inequalities

doi:10.1007/s11464-018-0733-9

Front. Math. China

2018, Vol. 13

Issue (6) : 1369-1396 https://doi.org/10.1007/s11464-018-0733-9

RESEARCH ARTICLE

Signal recovery under mutual incoherence property and oracle inequalities

Peng LI¹, Wengu CHEN²(

)

¹. Graduate School, China Academy of Engineering Physics, Beijing 100088, China
². Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

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Abstract

We consider the signal recovery through an unconstrained minimiza-tion in the framework of mutual incoherence property. A sufficient condition is provided to guarantee the stable recovery in the noisy case. Furthermore, oracle inequalities of both sparse signals and non-sparse signals are derived under the mutual incoherence condition in the case of Gaussian noises. Finally, we investigate the relationship between mutual incoherence property and robust null space property and find that robust null space property can be deduced from the mutual incoherence property.

Keywords Mutual incoherence property (MIP) Lasso Dantzig selector oracle inequality robust null space property (RNSP)

Corresponding Author(s): Wengu CHEN

Issue Date: 02 January 2019

Cite this article:

Peng LI,Wengu CHEN. Signal recovery under mutual incoherence property and oracle inequalities[J]. Front. Math. China, 2018, 13(6): 1369-1396.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0733-9
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I6/1369

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