Uncertainty Relations and Sparse Signal Recovery for Pairs of General Signal Sets
Artikel i vetenskaplig tidskrift, 2012

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.

uncertainty relations

signal recovery


orthogonal matching pursuit

frame theory

Basis pursuit


Patrick Kuppinger

Eidgenössische Technische Hochschule Zürich (ETH)

Giuseppe Durisi

Chalmers, Signaler och system, Kommunikations- och antennsystem, Kommunikationssystem

Helmut Bölcskei

Eidgenössische Technische Hochschule Zürich (ETH)

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 58 1 263 - 277 6012526


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