NDLI: A Geometrical Study of Matching Pursuit Parametrization

Content Provider	IEEE Xplore Digital Library
Author	Jacques, L. De Vleeschouwer, C.
Copyright Year	1991
Abstract	This paper studies the effect of discretizing the parametrization of a dictionary used for matching pursuit (MP) decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be applied. The main contribution of this paper is twofold. First, we prove that if a discrete dictionary reaches a minimal density criterion, then the corresponding discrete MP (dMP) is equivalent in terms of convergence to a weakened hypothetical continuous MP. Interestingly, the corresponding weakness factor depends on a density measure of the discrete dictionary. Second, we show that the insertion of a simple geometric gradient ascent optimization on the atom dMP selection maintains the previous comparison but with a weakness factor at least two times closer to unity than without optimization. Finally, we present numerical experiments confirming our theoretical predictions for decomposition of signals and images on regular discretizations of dictionary parametrizations.
Sponsorship	IEEE Signal Processing Society
Starting Page	2835
Ending Page	2848
Page Count	14
File Size	816476
File Format	PDF
ISSN	1053587X
Volume Number	56
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Matching pursuit algorithms Dictionaries Geometry Signal processing Prototypes Convergence Discrete wavelet transforms Density measurement Atomic measurements Pursuit algorithms Riemannian geometry dictionary matching pursuit (MP) optimization parametrization
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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