An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2003
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911217528864768 |
|---|---|
| author | Daubechies, Ingrid Defrise, Michel De Mol, Christine |
| author_facet | Daubechies, Ingrid Defrise, Michel De Mol, Christine |
| contents | We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the coefficients of such expansions, with 1 < or = p < or =2, still regularizes the problem. If p < 2, regularized solutions of such l^p-penalized problems will have sparser expansions, with respect to the basis under consideration. To compute the corresponding regularized solutions we propose an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. We also review some potential applications of this method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0307152 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Daubechies, Ingrid Defrise, Michel De Mol, Christine Functional Analysis Numerical Analysis We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the coefficients of such expansions, with 1 < or = p < or =2, still regularizes the problem. If p < 2, regularized solutions of such l^p-penalized problems will have sparser expansions, with respect to the basis under consideration. To compute the corresponding regularized solutions we propose an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. We also review some potential applications of this method. |
| title | An iterative thresholding algorithm for linear inverse problems with a sparsity constraint |
| topic | Functional Analysis Numerical Analysis |
| url | https://arxiv.org/abs/math/0307152 |