Superresolution via sparsity constraints
SIAM Journal on Mathematical Analysis
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Array Signal Processing: Concepts and Techniques
Array Signal Processing: Concepts and Techniques
Convex Optimization
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
Denoising by sparse approximation: error bounds based on rate-distortion theory
EURASIP Journal on Applied Signal Processing
Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
SIAM Journal on Numerical Analysis
Block-sparsity: Coherence and efficient recovery
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
On the reconstruction of block-sparse signals with an optimal number of measurements
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
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
An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem
IEEE Transactions on Signal Processing - Part II
Fast orthogonal least squares algorithm for efficient subset modelselection
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
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
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Why Simple Shrinkage Is Still Relevant for Redundant Representations?
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
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A problem that arises in slice-selective magnetic resonance imaging (MRI) radio-frequency (RF) excitation pulse design is abstracted as a novel linear inverse problem with a simultaneous sparsity constraint. Multiple unknown signal vectors are to be determined, where each passes through a different system matrix and the results are added to yield a single observation vector. Given the matrices and lone observation, the objective is to find a simultaneously sparse set of unknown vectors that approximately solves the system. We refer to this as the multiple-system single-output (MSSO) simultaneous sparse approximation problem. This manuscript contrasts the MSSO problem with other simultaneous sparsity problems and conducts an initial exploration of algorithms with which to solve it. Greedy algorithms and techniques based on convex relaxation are derived and compared empirically. Experiments involve sparsity pattern recovery in noiseless and noisy settings and MRI RF pulse design.