Stable Restoration and Separation of Approximately Sparse Signals

Christoph Studer; Richard G. Baraniuk

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arXiv · 1107.0420

Stable Restoration and Separation of Approximately Sparse Signals

Christoph Studer·Richard G. Baraniuk

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Abstract

This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. The algorithms and analytical recovery conditions consider varying degrees of signal and interference support-set knowledge. Particular applications covered by the proposed framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation/clipping, as well as image in-painting, super-resolution, and signal separation. Two application examples for audio and image restoration demonstrate the efficacy of the approach.

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Christoph Studer, Richard G. Baraniuk. 2011-07-03. Stable Restoration and Separation of Approximately Sparse Signals. https://arxiv.org/abs/1107.0420

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