Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Signal reconstruction in sensor arrays using sparse representations
Signal Processing - Sparse approximations in signal and image processing
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
DNA Array Decoding from Nonlinear Measurements by Belief Propagation
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
High-resolution radar via compressed sensing
IEEE Transactions on Signal Processing
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
A sparse signal reconstruction perspective for source localization with sensor arrays
IEEE Transactions on Signal Processing - Part II
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
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In this paper, we analyze the performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space. We formulate support recovery as a multiple-hypothesis testing problem and derive both upper and lower bounds on the probability of error for general measurement matrices, by using Chernoff bound and Fano's inequality, respectively. When applied to Gaussian measurement ensembles, these bounds give necessary and sufficient conditions to guarantee a vanishing probability of error for majority realizations of the measurement matrix. Our results offer surprising insights into sparse signal reconstruction based on their projections. For example, as far as support recovery is concerned, the well-known bound in compressive sensing is generally not sufficient if the Gaussian ensemble is used. Our study provides an alternative performance measure, one that is natural and important in practice, for signal recovery in compressive sensing as well as other application areas taking advantage of signal sparsity.