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On verifiable sufficient conditions for sparse signal recovery via ℓ1 minimization (2010).
| Content Provider | CiteSeerX |
|---|---|
| Author | Iouditski, Anatoli Nemirovski, Arkadi |
| Abstract | We discuss necessary and sufficient conditions for a sensing matrix to be “s-good ” – to allow for exact ℓ1-recovery of sparse signals with s nonzero entries when no measurement noise is present. Then we express the error bounds for imperfect ℓ1-recovery (nonzero measurement noise, nearly s-sparse signal, near-optimal solution of the optimization problem yielding the ℓ1-recovery) in terms of the characteristics underlying these conditions. Further, we demonstrate (and this is the principal result of the paper) that these characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse ℓ1-recovery and to efficiently computable upper bounds on those s for which a given sensing matrix is s-good. We establish also instructive links between our approach and the basic concepts of the Compressed Sensing theory, like Restricted Isometry or Restricted Eigenvalue properties. 1 |
| File Format | |
| Publisher Date | 2010-01-01 |
| Access Restriction | Open |
| Subject Keyword | Verifiable Sufficient Condition Sparse Signal Recovery Sensing Matrix Measurement Noise Sufficient Condition Instructive Link Compressed Sensing Theory Basic Concept Computable Upper Bound Eigenvalue Property Optimization Problem Nonzero Measurement Noise Sparse Signal S-sparse Signal Near-optimal Solution Nonzero Entry Principal Result |
| Content Type | Text |
