基于$l_q$-极小化($0<q\leq1$)的相干紧框架压缩感知
Compressed Sensing with coherent tight frames via $l_q$-minimization for $0<q\leq1$
AI总结：
针对信号在紧框架下稀疏的情况，提出一种与框架相干性无关的条件，通过最小化变换系数的$l_1$范数实现欠采样数据的精确恢复，并推广到$l_q$极小化($0<q<1$)，证明存在$q_0$使得对所有$q\in(0,q_0)$，$l_q$极小化解近似于真实信号。
摘要：
本文旨在从欠采样数据中重建信号，其中信号在紧框架意义下是稀疏的。我们提出了一个与紧框架相干性无关的条件，以保证通过变换系数的最小$l_1$范数从欠采样数据中精确恢复紧框架稀疏信号。这改进了文献[1]的结果。此外，还引入了$l_q$极小化方法($0<q<1$)。我们证明，在适当条件下，存在一个值$q_0\in(0,1]$，使得对于任意$q\in(0,q_0)$，$l_q$极小化的每个解都很好地逼近真实信号。特别地，当紧框架为单位矩阵或标准正交基时，本文得到的所有结果均出现在文献[13]和[26]中。
英文摘要：
Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee accurate recovery of signals which are sparse in the tight frame, from undersampled data with minimal $l_1$-norm of transform coefficients. This improves the result in [1]. Also, the $l_q$-minimization $(0<q<1)$ approaches are introduced. We show that under a suitable condition, there exists a value $q_0\in(0,1]$ such that for any $q\in(0,q_0)$, each solution of the $l_q$-minimization is approximately well to the true signal. In particular, when the tight frame is an identity matrix or an orthonormal basis, all results obtained in this paper appeared in [13] and [26].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
