New sufficient conditions of signal recovery with tight frames via $l_1$-analysis

Jianwen Huang; Jianjun Wang; Feng Zhang; Wendong Wang

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arXiv · 1710.11124

New sufficient conditions of signal recovery with tight frames via $l_1$-analysis

Jianwen Huang·Jianjun Wang·Feng Zhang·Wendong Wang

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Abstract

The paper discusses the recovery of signals in the case that signals are nearly sparse with respect to a tight frame $D$ by means of the $l_1$-analysis approach. We establish several new sufficient conditions regarding the $D$-restricted isometry property to ensure stable reconstruction of signals that are approximately sparse with respect to $D$. It is shown that if the measurement matrix $\Phi$ fulfils the condition $\delta_{ts}<t/(4-t)$ for $0<t<4/3$, then signals which are approximately sparse with respect to $D$ can be stably recovered by the $l_1$-analysis method. In the case of $D=I$, the bound is sharp, see Cai and Zhang's work \cite{Cai and Zhang 2014}. When $t=1$, the present bound improves the condition $\delta_s<0.307$ from Lin et al.'s reuslt to $\delta_s<1/3$.

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BibTeX RIS

Jianwen Huang, Jianjun Wang, Feng Zhang, Wendong Wang. 2017-10-30. New sufficient conditions of signal recovery with tight frames via $l_1$-analysis. https://arxiv.org/abs/1710.11124

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