Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
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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.
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- Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
Volume 9, Issue 3 , pp 317-334
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- Signal recovery algorithms
- Restricted isometry condition
- Uncertainty principle
- Basis pursuit
- Compressed sensing
- Orthogonal matching pursuit
- Signal recovery
- Sparse approximation
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