Revisiting maximal response-based local identification of overcomplete dictionaries
Revisiting maximal response-based local identification of overcomplete dictionaries
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DOI：
10.1109/sam.2016.7569722
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发表时间：
2016-07
期刊：
影响因子：
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通讯作者：
Z. Shakeri;W. Bajwa
中科院分区：
文献类型：
--
作者：
Z. Shakeri;W. Bajwa
本文重新讨论了使用所谓的最大响应准则（MRC）从训练样本中恢复局部邻域中的过完备字典的问题。虽然文献中已知 MRC 可用于局部邻域中字典的渐近精确恢复，但这些结果不允许对信号表示中的稀疏级别进行线性（在环境维度中）缩放。在本文中，利用一种新的证明技术来证明 MRC 实际上可以处理信号表示的线性稀疏性（模对数因子）。虽然这项工作的重点是渐近精确恢复，但可以以直接的方式使用相同的想法来加强涉及噪声观测和有限数量的训练样本的基于 MRC 的原始结果。
This paper revisits the problem of recovery of an overcomplete dictionary in a local neighborhood from training samples using the so-called maximal response criterion (MRC). While it is known in the literature that MRC can be used for asymptotic exact recovery of a dictionary in a local neighborhood, those results do not allow for linear (in the ambient dimension) scaling of sparsity levels in signal representations. In this paper, a new proof technique is leveraged to establish that MRC can in fact handle linear sparsity (modulo a logarithmic factor) of signal representations. While the focus of this work is on asymptotic exact recovery, the same ideas can be used in a straightforward manner to strengthen the original MRC-based results involving noisy observations and finite number of training samples.