Compressed sensing with coherent and redundant dictionaries
Compressed sensing with coherent and redundant dictionaries
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DOI：
10.1016/j.acha.2010.10.002
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发表时间：
2011-07-01
影响因子：
2.5
通讯作者：
Randall, Paige
中科院分区：
文献类型：
--
作者：
Candes, Emmanuel J.;Eldar, Yonina C.;Randall, Paige
本文提出了新的结果，有关信号的恢复欠采样数据在常见的情况下，这些信号是不是稀疏的正交基或不相干的字典，但在一个真正的冗余字典。因此，这项工作弥补了文献中的空白，不仅表明压缩感知在这种情况下是通过的，而且还表明通过l（1）-分析优化问题可以实现准确的恢复。我们引入了一个条件的测量/传感矩阵，这是一个自然的推广，现在众所周知的限制等距属性，并保证准确的恢复信号，几乎稀疏（可能）高度过完备和连贯的字典。这个条件对字典没有不连贯的限制，我们的结果可能是第一个这样的。我们讨论了实际的例子和我们的结果对这些应用的影响，并补充我们的研究，证明了潜在的l（1）-分析等问题。(C)2010年爱思唯尔公司All rights reserved.
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary. This work thus bridges a gap in the literature and shows not only that compressed sensing is via)le in this context, but also that accurate recovery is possible via an l(1)-analysis optimization problem. We introduce a condition on the measurement/sensing matrix, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are nearly sparse in (possibly) highly overcomplete and coherent dictionaries. This condition imposes no incoherence restriction on the dictionary and our results may be the first of this kind. We discuss practical examples and the implications of our results on those applications, and complement our study by demonstrating the potential of l(1)-analysis for such problems. (C) 2010 Elsevier Inc. All rights reserved.