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Theoretical Results on Sparse Representations of Multiple-Measurement Vectors.
- Source :
-
IEEE Transactions on Signal Processing . Dec2006, Vol. 54 Issue 12, p4634-4643. 10p. 3 Graphs. - Publication Year :
- 2006
-
Abstract
- 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 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 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *VECTOR analysis
*SPARSE matrices
*RANDOM matrices
*MATHEMATICS
*VECTOR spaces
Subjects
Details
- Language :
- English
- ISSN :
- 1053587X
- Volume :
- 54
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Signal Processing
- Publication Type :
- Academic Journal
- Accession number :
- 23838786
- Full Text :
- https://doi.org/10.1109/TSP.2006.881263