Sparse Signal Recovery in Hilbert Spaces

Graeme Pope; Helmut Bölcskei

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arXiv · 1205.4583

Sparse Signal Recovery in Hilbert Spaces

Graeme Pope·Helmut Bölcskei

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Abstract

This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the number of (possibly infinite-dimensional) subspaces participating in the signal's representation. Our general results recover uncertainty relations and coherence-based recovery thresholds for sparse signals, block-sparse signals, multi-band signals, signals in shift-invariant spaces, and signals in finite unions of (possibly infinite-dimensional) subspaces. Moreover, we improve upon and generalize several of the existing results and, in many cases, we find shortened and simplified proofs.

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Graeme Pope, Helmut Bölcskei. 2012-05-21. Sparse Signal Recovery in Hilbert Spaces. https://arxiv.org/abs/1205.4583

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