Greed is good: Algorithmic results for sparse approximation

Greed is good: Algorithmic results for sparse approximation (2004)

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by Joel A. Tropp

Venue:	IEEE Trans. Inform. Theory
Citations:	327 - 6 self

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Datum	Value	Source
TITLE	Greed is good: Algorithmic results for sparse approximation	INFERENCE
AUTHOR NAME	Joel A. Tropp	SVM HeaderParse 0.2
ABSTRACT	Abstract. This article presents new results on using a greedy algorithm, Orthogonal Matching Pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It contains a single sufficient condition under which both OMP and Donoho’s Basis Pursuit paradigm (BP) can recover an exactly sparse signal. It leverages this theory to show that both OMP and BP can recover all exactly sparse signals from a wide class of dictionaries. These quasi-incoherent dictionaries offer a natural generalization of incoherent dictionaries, and the Babel function is introduced to quantify the level of incoherence. Indeed, this analysis unifies all the recent results on BP and extends them to OMP. Furthermore, the paper develops a sufficient condition under which OMP can retrieve the common atoms from all optimal representations of a nonsparse signal. From there, it argues that Orthogonal Matching Pursuit is an approximation algorithm for the sparse problem over a quasiincoherent dictionary. That is, for every input signal, OMP can calculate a sparse approximant whose error is only a small factor worse than the optimal error which can be attained with the same number of terms. 1.	SVM HeaderParse 0.2
YEAR	2004	INFERENCE
VENUE	IEEE Trans. Inform. Theory	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	2231--2242	INFERENCE
VOLUME	50	INFERENCE
CITATIONS	28 found	ParsCit 1.0