NDLI: Blind Compressed Sensing

Content Provider	IEEE Xplore Digital Library
Author	Gleichman, S. Eldar, Y.C.
Copyright Year	1963
Description	The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is essential for the recovery process. This work introduces the concept of blind compressed sensing, which avoids the need to know the sparsity basis in both the sampling and the recovery process. We suggest three possible constraints on the sparsity basis that can be added to the problem in order to guarantee a unique solution. For each constraint, we prove conditions for uniqueness, and suggest a simple method to retrieve the solution. We demonstrate through simulations that our methods can achieve results similar to those of standard compressed sensing, which rely on prior knowledge of the sparsity basis, as long as the signals are sparse enough. This offers a general sampling and reconstruction system that fits all sparse signals, regardless of the sparsity basis, under the conditions and constraints presented in this work.
Sponsorship	IEEE Information Theory Society
Starting Page	6958
Ending Page	6975
Page Count	18
File Size	600545
File Format	PDF
ISSN	00189448
Volume Number	57
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sparse matrices Dictionaries Compressed sensing Indexes Sparks Null space Matching pursuit algorithms sparse representation Blind reconstruction compressed sensing dictionary learning
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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