Regularization with non-convex separable constraints

Inverse Problems

Volumn 25, Issue 8, 2009, Pages

  Bredies, Kristian ^a   Lorenz, Dirk A ^b  

^a UNIVERSITY OF GRAZ   (Austria)

^b TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE RATES; ERROR ESTIMATES; NOISE LEVELS; NONCONVEX FUNCTIONS; NONLINEAR ILL-POSED PROBLEMS; SEQUENCE SPACE; SPARSITY CONSTRAINTS;

EID: 70350634124     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/25/8/085011     Document Type: Article

References (38)

1. Bonesky T 2009 Morozov's discrepancy principle and Tikhonov-type functionals Inverse Problems 25 015015(11pp)
2. Bonesky T, Bredies K, Lorenz D A and Maass P 2007 A generalized conditional gradient method for nonlinear operator equations with sparsity constraints Inverse Problems 23 2041-58
3. Bredies K 2009 A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space Inverse Problems 25 015005 (20pp)
4. Bredies K 2009 An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space J. Inverse Ill Posed Probl. 17 19-28
5. Bredies K and Lorenz D A 2008 Iterated hard shrinkage for minimization problems with sparsity constraints SIAM J. Sci. Comput 30 657-83
6. Bredies K and Lorenz D A 2008 Linear convergence of iterative soft-thresholding J. Fourier Anal. Appl. 14 813-37
7. Bredies K and Lorenz D A 2009 Minimization of non-smooth, non-convex functionals by iterative thresholding (preprint DFG priority programme 1324 10)
8. Bredies K, Lorenz D A and Maass P 2008 A generalized conditional gradient method and its connection to an iterative shrinkage method Comput. Optim. Appl. 42 173-93
9. Burger M and Osher S J 2004 Convergence rates of convex variational regularization Inverse Problems 20 1411-20
10. Burger M, Resmerita E and Lin He 2007 Error estimation for Bregman iterations and inverse scale space methods in image restoration (Special Issue on Industrial Geometry) Computing 81 109-35
11. Chambolle A 2004 An algorithm for total variation minimization and applications J. Math. Imaging. Vis 20 89-97
12. Chartrand R 2007 Exact reconstructions of sparse signals via nonconvex minimization IEEE Signal Process. Lett. 14 707-10
13. Combettes P L and Wajs V R 2005 Signal recovery by proximal forward-backward splitting Multiscale Model. Simul. 4 1168-200
14. Daubechies I, Defrise M and De Mol C 2004 An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Commun Pure Appl. Math. 57 1413-57
15. Daubechies I, Fornasier M and Loris I 2008 Accelerated projected gradient method for linear inverse problems with sparsity constraints J. Fourier Anal. Appl. 14 764-92
16. Donoho D L, Johnstone I M, Hoch J C and Stern A S 1992 Maximal entropy and the nearly black object J. R. Stat. Soc. Series B 54 41-81
17. Engl H W, Hanke M and Neubauer Andreas 2000 Regularization of Inverse Problems (Mathematics and its Applications vol 375) (Dordrecht: Kluwer)
18. Engl H W and Landl G 1993 Convergence rates for maximum entropy regularization SIAM J. Numer. Anal. 30 1509-36
19. Figueiredo M A T, Nowak R D and Wright S J 2007 Gradient projection for sparse reconstruction: applications to compressed sensing and other inverse problems IEEE J. Sel. Top. Signal Process. 4 586-97
20. q penalty term Industrial Geometry report 74
21. q penalty term Inverse Problems 24 055020 (13pp)
22. Griesse R and Lorenz D A 2008 A semismooth Newton method for Tikhonov functionals with sparsity constraints Inverse Problems 24 035007 (19pp)
23. Hein T A 2008 Convergence rates for regularization of ill-posed problems in Banach spaces by approximate source conditions Inverse Problems 24 045007 (10pp)
24. Hintermüller M and Kunisch K 2004 Total bounded variation regularization as a bilaterally constrained optimization problem SIAM J. Appl. Math. 64 1311-33
25. Hofmann B, Kaltenbacher B, Poeschl C and Scherzer O 2007 A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators Inverse Problems 23 987-1010
26. Lorenz D A 2008 Convergence rates and source conditions for Tikhonov regularization with sparsity constraints J. Inverse Ill-Posed Problems 16 463-78
27. Lorenz D A 2009 On the role of sparsity in inverse problems J. Inverse Ill Posed Problems 17 61-8
28. Lorenz D A and Trede D 2008 Optimal convergence rates for Tikhonov regularization in Besov scales Inverse Problems 24 055010 (14pp)
29. Pöschl C 2009 An overview on convergence rates for Tikhonov regularization methods for non-linear operators J. Inverse Ill Posed Problems 17 77-84
30. Ramlau R 2008 Regularization properties of Tikhonov regularization with sparsity constraints Electron. Trans. Numerical Anal. 30 54-74
31. Ramlau R and Teschke G 2006 A Tikhonov-based projection iteration for nonlinear ill-posed problems with sparsity constraints Numer. Math. 104 177-203
32. Resmerita E 2005 Regularization of ill-posed problems in Banach spaces: convergence rates Inverse Problems 21 1303-14
33. Resmerita E and Scherzer O 2006 Error estimates for non-quadratic regularization and the relation to enhancement Inverse Problems 22 801-14
34. Schirotzek W 2007 Nonsmooth Analysis (Berlin: Springer)
35. Schöpfer F, Louis A K and Schuster T 2006 Nonlinear iterative methods for linear ill-posed problems in Banach spaces Inverse Problems 22 311-29
36. Schuster T, Maass P, Bonesky T, Kazimierski K S and Schöpfer F 2008 Minimization of Tikhonov functionals in Banach spaces Abstract Appl. Anal. 2008 192679 (19 pp)
37. Vogel C R and Acar R 1994 Analysis of bounded variation penalty methods for ill-posed problems Inverse Problems 10 1217-29
38. Zarzer C A 2009 On Tikhonov regularization with non-convex sparsity constraints Inverse Problems 25 025006