Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Convex Optimization
Recovery of sparse representations by polytope faces pursuit
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On Polar Polytopes and the Recovery of Sparse Representations
IEEE Transactions on Information Theory
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Compressed sensing, also known as compressive sampling, is an approach to the measurement of signals which have a sparse representation, that can reduce the number of measurements that are needed to reconstruct the signal. The signal reconstruction part requires efficient methods to perform sparse reconstruction, such as those based on linear programming. In this paper we present a method for sparse reconstruction which is an extension of our earlier Polytope Faces Pursuit algorithm, based on the polytope geometry of the dual linear program. The new algorithm adds several basis vectors at each stage, in a similar way to the recent Stagewise Orthogonal Matching Pursuit (StOMP) algorithm. We demonstrate the application of the algorithm to some standard compressed sensing problems.