Stable Restoration and Separation of Approximately Sparse Signals

Details Stable Restoration and Separation of Approximately Sparse Signals Stable Restoration and Separation of Approximately Sparse Signals

2011-07-03

arxiv.org/abs/1107.0420v1

Computer Science

Information Theory

submitted to Applied and Computational Harmonic Analysis (ACHA)

Scientific paper

This paper develops new theory and algorithms to recover signals that are approximately sparse in some general (i.e., basis, frame, over-complete, or in-complete) dictionary but corrupted by a combination of measurement noise and interference having a sparse representation in a second general dictionary. Particular applications covered by our framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation, as well as image in-painting, super-resolution, and signal separation. We develop efficient recovery algorithms and deterministic conditions that guarantee stable restoration and separation. Two application examples demonstrate the efficacy of our approach.

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