Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Algorithms for simultaneous sparse approximation: part II: Convex relaxation
Signal Processing - Sparse approximations in signal and image processing
On the reconstruction of block-sparse signals with an optimal number of measurements
IEEE Transactions on Signal Processing
A sparse signal reconstruction perspective for source localization with sensor arrays
IEEE Transactions on Signal Processing - Part II
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors
IEEE Transactions on Signal Processing
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors
IEEE Transactions on Signal Processing - Part I
Sparse solutions to linear inverse problems with multiple measurement vectors
IEEE Transactions on Signal Processing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Recovery of short, complex linear combinations via ℓ1 minimization
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely studied in compressed sensing.We study the recovery properties of two algorithms for problems with noiseless data and exact-sparse representation. First, we show that recovery using sum-of-norm minimization cannot exceed the uniform-recovery rate of sequential SMV using l1 minimization, and that there are problems that can be solved with one approach, but not the other. Second, we study the performance of the ReMBo algorithm (M. Mishali and Y. Eldar, "Reduce and boost: Recovering arbitrary sets of jointly sparse vectors," IEEE Trans. Signal Process., vol. 56, no. 10, 4692-4702, Oct. 2008) in combination with l1 minimization, and show how recovery improves as more measurements are taken. From this analysis, it follows that having more measurements than the number of linearly independent nonzero rows does not improve the potential theoretical recovery rate.