Computational Methods for Sparse Solution of Linear Inverse Problems

The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the...

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Bibliographic Details
Published in:Proceedings of the IEEE 2010-06, Vol.98 (6), p.948-958
Main Authors: Tropp, Joel A., Wright, Stephen J.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Approximation algorithms
Collection
Compressed sensing
Computation
convex optimization
Dictionaries
Electrical engineering
Inverse problems
Least squares approximation
matching pursuit
Matching pursuit algorithms
Mathematical analysis
Mathematical models
Mathematics
Signal processing
Signal processing algorithms
sparse approximation
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Summary:The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications.
ISSN:0018-9219
1558-2256
DOI:10.1109/JPROC.2010.2044010