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Theoretical results on sparse representations of multiple-measurement vectors (2006)
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| Venue: | IEEE Trans. Signal Process |
| Citations: | 142 - 2 self |
BibTeX
@ARTICLE{Chen06theoreticalresults,
author = {Jie Chen and Xiaoming Huo},
title = {Theoretical results on sparse representations of multiple-measurement vectors},
journal = {IEEE Trans. Signal Process},
year = {2006},
pages = {4634--4643}
}
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Abstract
Abstract — Multiple measurement vector (MMV) is a relatively new problem in sparse representations. Efficient methods have been proposed. Considering many theoretical results that are available in a simple case – single measure 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 ℓ0-norm like criterion and an ℓ1-norm like criterion. The consequent equivalence between the ℓ0-norm approach and the ℓ1-norm approach indicates a computationally efficient way of finding the sparsest representation in an over-complete 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 theoretical advances in probability. The connections will be discussed.
Keyphrases
sparse representation multiple-measurement vector theoretical result new problem many theoretical result certain condition over-complete dictionary greedy algorithm theoretical analysis orthogonal matching pursuit efficient way simple case single measure vector efficient method new result 1-norm approach computational efficiency 0-norm approach recent theoretical advance consequent equivalence proved theorem abstract multiple measurement vector additional information
