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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| Published in | Proceedings of the IEEE Vol. 98; no. 6; pp. 948 - 958 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.06.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Wright, Stephen J. Tropp, Joel A. |
| Author_xml | – sequence: 1 givenname: Joel A. surname: Tropp fullname: Tropp, Joel A. email: jtropp@acm.caltech.edu organization: Applied and Computational Mathematics, Firestone Laboratories MC 217-50, California Institute of Technology, Pasadena, CA, USA – sequence: 2 givenname: Stephen J. surname: Wright fullname: Wright, Stephen J. email: swright@cs.wisc.edu organization: Computer Sciences Department, University of Wisconsin, Madison , WI, USA |
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| CODEN | IEEPAD |
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| SubjectTerms | 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 Statistics |
| Title | Computational Methods for Sparse Solution of Linear Inverse Problems |
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