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New upper bounds of cumulative coherence for $\ell_{1-2}$-minimization in compressed sensing
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  • Youwei Xie,
  • Kaihao Liang,
  • Meijiao Zhang,
  • Shaohua Xie
Youwei Xie
Quanzhou University of Information Engineering
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Kaihao Liang
Zhongkai University of Agriculture and Engineering
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Meijiao Zhang
Quanzhou University of Information Engineering
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Shaohua Xie
Sun Yat-Sen University

Corresponding Author:xieshh28@mail2.sysu.edu.cn

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Abstract

This paper focuses on the compressed sensing $\ell_{1-2}$-minimization problem and develops new bounds on cumulative coherence $\mu_1(s)$. We point out that if cumulative coherence $\mu_1(s-1)$ and $\mu_1(2s-1)$ satisfy $(\ref{eq:EqNo2})$, or cumulative coherence $ \mu_1(2s-1)$ satisfies $(\ref{eq:EqNo11})$ then the sparse signal can via $\ell_{1-2}$-minimization problem stably recover in noise model and exact recovery in free noise model.