Matrix analysis
Uncertainty principles and signal recovery
SIAM Journal on Applied Mathematics
Signal recovery and the large sieve
SIAM Journal on Applied Mathematics
Matrix computations (3rd ed.)
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Array Signal Processing: Concepts and Techniques
Array Signal Processing: Concepts and Techniques
Universal distributed sensing via random projections
Proceedings of the 5th international conference on Information processing in sensor networks
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
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)
Denoising by sparse approximation: error bounds based on rate-distortion theory
EURASIP Journal on Applied Signal Processing
Deterministic constructions of compressed sensing matrices
Journal of Complexity
Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
SIAM Journal on Numerical Analysis
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
Sublinear compressive sensing reconstruction via belief propagation decoding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Linear Regression With a Sparse Parameter Vector
IEEE Transactions on Signal Processing
A sparse signal reconstruction perspective for source localization with sensor arrays
IEEE Transactions on Signal Processing - Part II
Space-time fading channel estimation and symbol detection inunknown spatially correlated noise
IEEE Transactions on Signal Processing
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
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
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Journal of Approximation Theory
Hi-index | 754.84 |
The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower bounds on the probability of error are derived for general measurement matrices, by using the Chernoff bound and Fano's inequality, respectively. The upper bound shows that the performance is determined by a quantity measuring the measurement matrix incoherence, while the lower bound reveals the importance of the total measurement gain. The lower bound is applied to derive the minimal number of samples needed for accurate direction-of-arrival (DOA) estimation for a sparse representation based algorithm. When applied to Gaussian measurement ensembles, these bounds give necessary and sufficient conditions for a vanishing probability of error for majority realizations of the measurement matrix. Our results offer surprising insights into sparse signal recovery. For example, as far as support recovery is concerned, the well-known bound in Compressive Sensing with the Gaussian measurement matrix is generally not sufficient unless the noise level is low. Our study provides an alternative performance measure, one that is natural and important in practice, for signal recovery in Compressive Sensing and other application areas exploiting signal sparsity.