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Full-Text Articles in Physical Sciences and Mathematics
Signal Space Cosamp For Sparse Recovery With Redundant Dictionaries, Mark A. Davenport, Deanna Needell, Michael B. Wakin
Signal Space Cosamp For Sparse Recovery With Redundant Dictionaries, Mark A. Davenport, Deanna Needell, Michael B. Wakin
CMC Faculty Publications and Research
Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an orthonormal basis. In practice, however, there are many signals that cannot be sparsely represented or approximated using an orthonormal basis, but that do have sparse representations in a redundant dictionary. Standard results in CS can sometimes be extended to handle this case provided that the dictionary is sufficiently incoherent or well conditioned, but these approaches fail to address the case of a truly …
Uniform Uncertainty Principle And Signal Recovery Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin
Uniform Uncertainty Principle And Signal Recovery Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin
CMC Faculty Publications and Research
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.