Name
Abstract | ||
|---|---|---|
We explore the application of a homotopy continuation-based method for sparse signal representation in overcomplete dictionaries. Our problem setup is based on the basis pursuit framework, which involves a convex optimization problem consisting of terms enforcing data fidelity and sparsity, balanced by a regularization parameter. Choosing a good regularization parameter in this framework is a challenging task. We describe a homotopy continuation-based algorithm to efficiently find and trace all solutions of basis pursuit as a function of the regularization parameter. In addition to providing an attractive alternative to existing optimization methods for solving the basis pursuit problem, this algorithm can also be used to provide an automatic choice for the regularization parameter, based on prior information about the desired number of non-zero components in the sparse representation. Our numerical examples demonstrate the effectiveness of this algorithm in accurately and efficiently generating entire solution paths for basis pursuit, as well as producing reasonable regularization parameter choices. Furthermore, exploring the resulting solution paths in various operating conditions reveals insights about the nature of basis pursuit solutions. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1109/ICASSP.2005.1416408 | 2005 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1-5: SPEECH PROCESSING |
Keywords | Field | DocType |
signal processing,basis pursuit,sparse representation,dictionaries,signal generators,quadratic programming,operant conditioning,convex optimization | Signal processing,Mathematical optimization,Fidelity,Basis pursuit denoising,Computer science,Sparse approximation,Basis pursuit,Regularization (mathematics),Quadratic programming,Convex optimization | Conference |
ISSN | Citations | PageRank |
1520-6149 | 99 | 15.70 |
References | Authors | |
5 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dmitry M. Malioutov | 1 | 1052 | 86.85 |
| Müjdat Çetin | 2 | 1342 | 112.26 |
| Alan S. Willsky | 3 | 7466 | 847.01 |