An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space

Journal of Inverse and Ill-Posed Problems

Volumn 17, Issue 1, 2009, Pages 19-26

  Bredies, K ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

Banach space; Convergence analysis; Generalized gradient projection method; Iterative thresholding; Sparsity constraints

Indexed keywords

EID: 59449085134     PISSN: 09280219     EISSN: None     Source Type: Journal    
DOI: 10.1515/JIIP.2009.003     Document Type: Article

References (12)

1. Y. I. Alber, A. N. Iusem, and M. V. Solodov, Minimization of nonsmooth convex functionals in Banach spaces. Journal of Convex Analysis 4, 2 (1997), 235-255.
2. D. Azú and J.-P. Penot, Uniformly convex and uniformly smooth convex functions. Annales de la faculté des Sciences de Toulouse Sér. 6 4, 4 (1995), 705-730.
3. K. Bredies, A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space. Inverse Problems 25 (2009). Article ID 015005.
4. K. Bredies and D. A. Lorenz, Iterated hard shrinkage for minimization problems with sparsity constraints. SIAM Journal on Scientific Computing 30, 2 (2008), 657-683.
5. K. Bredies and D. A. Lorenz, Linear convergence of iterated soft-thresholding. Journal of Fourier Analysis and Applications 14, 5-6 (2008), 813-837.
6. K. Bredies, D. A. Lorenz, and P. Maass, A generalized conditional gradient method and its connection to an iterative shrinkage method. Computational Optimization and Applications (to appear).
7. P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting. Multiscale Modeling and Simulation 4, 4 (2005), 1168-1200.
8. I. Daubechies, M. Defrise, and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications in Pure and Applied Mathematics 57, 11 (2004), 1413-1457. (Pubitemid 39427442)
9. I. Daubechies, M. Fornasier, and I. Loris, Accelerated projected gradient method for linear inverse problems with sparsity constraints. Journal of Fourier Analysis and Applications 14, 5-6 (2008), 764-792.
10. J. C. Dunn, Global and asymptotic convergence rate estimates for a class of projected gradient processes. SIAM Journal on Control and Optimization 19, 3 (1981), 368-400.
11. T. Schuster, P. Maass, T. Bonesky, K. S. Kazimierski, and F. Schöpfer, Minimization of Tikhonov functionals in Banach spaces. Abstract and Applied Analysis (2008). Article ID 192679.
12. Z. B. Xu and G. F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces. Journal of Mathematical Analysis and Applications 157, 1 (1991), 189-210.