NDLI: Tree-Based Pursuit: Algorithm and Properties

Content Provider	IEEE Xplore Digital Library
Author	Jost, P. Vandergheynst, P. Frossard, P.
Copyright Year	1991
Abstract	This paper proposes a tree-based pursuit algorithm that efficiently trades off complexity and approximation performance for overcomplete signal expansions. Finding the sparsest representation of a signal using a redundant dictionary is, in general, an NP-hard problem. Even suboptimal algorithms such as Matching Pursuit remain highly complex. We propose a structuring strategy that can be applied to any redundant set of functions, and which basically groups similar atoms together. A measure of similarity based on coherence allows for representing a highly redundant subdictionary of atoms by a unique element, called molecule. When the clustering is applied recursively on atoms and then on molecules, it naturally leads to the creation of a tree structure. We then present a new pursuit algorithm that uses the structure created by clustering as a decision tree. This tree-based algorithm offers important complexity reduction with respect to Matching Pursuit, as it prunes important parts of the dictionary when traversing the tree. Recent results on incoherent dictionaries are extended to molecules, while the true highly redundant nature of the dictionary stays hidden by the tree structure. We then derive recovery conditions on the structured dictionary, under which tree-based pursuit is guaranteed to converge. Experimental results finally show that the gain in complexity offered by tree-based pursuit does in general not have a high penalty on the approximation performance. They show that the dimensionality of the problem is reduced thanks to the tree construction, without significant loss of information
Sponsorship	IEEE Signal Processing Society
Starting Page	4685
Ending Page	4697
Page Count	13
File Size	1301705
File Format	PDF
ISSN	1053587X
Volume Number	54
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Pursuit algorithms Dictionaries Matching pursuit algorithms Signal processing algorithms Atomic measurements NP-hard problem Tree data structures Signal analysis Algorithm design and analysis Computational complexity tree search Clustering greedy algorithms matching pursuit redundant expansions sparse approximation
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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