Accelerated projected gradient method for linear inverse problems with sparsity constraints
Publication
, Journal Article
Daubechies, I; Fornasier, M; Loris, I
Published in: Journal of Fourier Analysis and Applications
December 1, 2008
Regularization of ill-posed linear inverse problems via ℓ1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an ℓ1 penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to ℓ1-constraints, using a gradient method, with projection on ℓ1-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration. © 2008 Birkhäuser Boston.
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Published In
Journal of Fourier Analysis and Applications
DOI
ISSN
1069-5869
Publication Date
December 1, 2008
Volume
14
Issue
5-6
Start / End Page
764 / 792
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
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Daubechies, I., Fornasier, M., & Loris, I. (2008). Accelerated projected gradient method for linear inverse problems with sparsity constraints. Journal of Fourier Analysis and Applications, 14(5–6), 764–792. https://doi.org/10.1007/s00041-008-9039-8
Daubechies, I., M. Fornasier, and I. Loris. “Accelerated projected gradient method for linear inverse problems with sparsity constraints.” Journal of Fourier Analysis and Applications 14, no. 5–6 (December 1, 2008): 764–92. https://doi.org/10.1007/s00041-008-9039-8.
Daubechies I, Fornasier M, Loris I. Accelerated projected gradient method for linear inverse problems with sparsity constraints. Journal of Fourier Analysis and Applications. 2008 Dec 1;14(5–6):764–92.
Daubechies, I., et al. “Accelerated projected gradient method for linear inverse problems with sparsity constraints.” Journal of Fourier Analysis and Applications, vol. 14, no. 5–6, Dec. 2008, pp. 764–92. Scopus, doi:10.1007/s00041-008-9039-8.
Daubechies I, Fornasier M, Loris I. Accelerated projected gradient method for linear inverse problems with sparsity constraints. Journal of Fourier Analysis and Applications. 2008 Dec 1;14(5–6):764–792.
Published In
Journal of Fourier Analysis and Applications
DOI
ISSN
1069-5869
Publication Date
December 1, 2008
Volume
14
Issue
5-6
Start / End Page
764 / 792
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics