Theoretical results on sparse representations of multiple-measurement vectors
Theoretical results on sparse representations of multiple-measurement vectors
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DOI：
10.1109/tsp.2006.881263
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发表时间：
2006-12-01
影响因子：
5.4
通讯作者：
Huo, Xiaoming
中科院分区：
文献类型：
--
作者：
Chen, Jie;Huo, Xiaoming
多测量向量的稀疏表示是稀疏表示中一个较新的问题。已经提出了有效的方法。尽管在简单的情况下（单测量向量（SMV））可以获得许多理论结果，但缺乏有关MMV的理论分析。本文将SMV的一些已知结果推广到MMV。其中一些新的结果利用额外的信息在制定MMV。我们考虑了在l（0）-类范数准则和l（1）-类范数准则下的唯一性。l（0）-范数方法和l（1）-范数方法之间的结果等价性指示了在冗余字典中找到稀疏表示的计算上有效的方式。对于贪婪算法，证明了在一定条件下，正交匹配追踪（OMP）可以找到MMV的稀疏表示与计算效率，就像在SMV。模拟结果表明，所证明的定理的预测往往是非常保守的，这是一致的随机矩阵理论的基础上的概率分析的一些最新进展。我们将讨论这些联系。
The sparse representation of a multiple-measurement vector (MMV) is a relatively new problem in sparse representation. Efficient methods have been proposed. Although many theoretical results that are available in a simple case-single-measurement vector (SMV)-the theoretical analysis regarding MMV is lacking. In this paper, some known results of SMV are generalized to MMV. Some of these new results take advantages of additional information in the formulation of MMV. We consider the uniqueness under both an l(0)-norm-like criterion and an l(1)-norm-like criterion. The consequent equivalence between the l(0)-norm approach and the l(1)-norm approach indicates a computationally efficient way of finding the sparsest representation in a redundant dictionary. For greedy algorithms, it is proven that under certain conditions, orthogonal matching pursuit (OMP) can find the sparsest representation of an MMV with computational efficiency, just like in SMV. Simulations show that the predictions made by the proved theorems tend to be very conservative; this is consistent with some recent advances in probabilistic analysis based on random matrix theory. The connections will be discussed.