NDLI: An improved FOCUSS-based learning algorithm for solving sparse linear inverse problems

Content Provider	IEEE Xplore Digital Library
Author	Murray, J.F. Kreutz-Delgado, K.
Copyright Year	2001
Description	Author affiliation: Dept. of Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA, USA (Murray, J.F.)
Abstract	We develop an improved algorithm for solving blind sparse linear inverse problems where both the dictionary (possibly overcomplete) and the sources are unknown. The algorithm is derived in the Bayesian framework by the maximum a posteriori method, with the choice of prior distribution restricted to the class of concave/Schur-concave functions, which has been shown previously to be a sufficient condition for sparse solutions. This formulation leads to a constrained and regularized minimization problem which can be solved in part using the FOCUSS (focal underdetermined system solver) algorithm for vector selection. We introduce three key improvements in the algorithm: an efficient way of adjusting the regularization parameter; column normalization that restricts the learned dictionary; reinitialization to escape from local optima. Experiments were performed using synthetic data with matrix sizes up to 64/spl times/128; the algorithm solves the blind identification problem, recovering both the dictionary and the sparse sources. The improved algorithm is much more accurate than the original FOCUSS-dictionary learning algorithm when using large matrices. We also test our algorithm on natural images, and show that a learned overcomplete representation can encode the data more efficiently than a complete basis at the same level of accuracy.
Starting Page	347
Ending Page	351
File Size	480906
Page Count	5
File Format	PDF
ISBN	078037147X
ISSN	10586393
DOI	10.1109/ACSSC.2001.986949
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-11-04
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Inverse problems Dictionaries Focusing Sparse matrices Algorithm design and analysis Independent component analysis Testing Image reconstruction Pattern recognition Bayesian methods
Content Type	Text
Resource Type	Article
Subject	Signal Processing Computer Networks and Communications

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