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
Characterization of oblique dual frame pairs
EURASIP Journal on Applied Signal Processing
Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Uncertainty relations for shift-invariant analog signals
IEEE Transactions on Information Theory
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors
IEEE Transactions on Signal Processing
Nonlinear and Nonideal Sampling: Theory and Methods
IEEE Transactions on Signal Processing
A Theory for Sampling Signals From a Union of Subspaces
IEEE Transactions on Signal Processing
A minimum squared-error framework for generalized sampling
IEEE Transactions on Signal Processing - Part I
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
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Block-sparse signals: uncertainty relations and efficient recovery
IEEE Transactions on Signal Processing
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Sparse signal representations have gained wide popularity in recent years. In many applications the data can be expressed using only a few nonzero elements in an appropriate expansion. In this paper, we study a block-sparse model, in which the nonzero coefficients are arranged in blocks. To exploit this structure. we redefine the standard (NP-hard) sparse recovery problem, based on which we propose a convex relaxation in the form of a mixed l2/l1 program. Isometry-based analysis is used to prove equivalence of the solution to that of the optimal program, under certain mild conditions. We further establish the robustness of our algorithm to mismodeling and bounded noise. We then present theoretical arguments and numerical experiments demonstrating the improved recovery performance of our method in comparison with sparse reconstruction that does not incorporate a block structure. The results are then applied to two related problems. The first is that of simultaneous sparse approximation. Our results can be used to prove isometry-based equivalence properties for this setting. In addition, we propose an alternative approach to acquire the measurements, that leads to performance improvement over standard methods. Finally, we show how our results can be used to sample signals in a finite structured union of subspaces, leading to robust and efficient recovery algorithms.