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Uncertainty Relations and Sparse Signal Recovery for Pairs of General Signal Sets

Patrick Kuppinger ; Giuseppe Durisi (Institutionen för signaler och system, Kommunikationssystem) ; Helmut Bölcskei
IEEE Transactions on Information Theory (0018-9448). Vol. 58 (2012), 1, p. 263 - 277 .
[Artikel, refereegranskad vetenskaplig]

We present an uncertainty relation for the representation of signals in two different general (possibly redundant or incomplete) signal sets. Specifically, our results improve on the well-known (1+1/d)/2-threshold for dictionaries with coherence d by up to a factor of two. Furthermore, the new uncertainty relation is shown to lead to improved sparsity thresholds for recovery of signals that are sparse in general dictionaries. Furthermore, we provide probabilistic recovery guarantees for pairs of general dictionaries that also allow us to understand which parts of a general dictionary one needs to randomize over to ``weed out'' the sparsity patterns that prohibit breaking the square-root bottleneck.This uncertainty relation is relevant for the analysis of signals containing two distinct features each of which can be described sparsely in a suitable general signal set.

Nyckelord: Basis pursuit; frame theory; orthogonal matching pursuit; signal recovery; sparsity; uncertainty relations

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Denna post skapades 2011-09-14. Senast ändrad 2015-01-29.
CPL Pubid: 146195


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