Perturbation resilience and superiorization of iterative algorithms

Inverse Problems

Volumn 26, Issue 6, 2010, Pages

  Censor, Y ^a   Davidi, R ^b   Herman, G T ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b City University of New York   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER MEMORIES; COMPUTER RESOURCES; CONVEX FEASIBILITY PROBLEM; CONVEX SET; EXECUTION TIME; FINITE NUMBER; IMAGE RECONSTRUCTION FROM PROJECTIONS; ITERATIVE ALGORITHM; MATHEMATICAL FORMS; OPTIMIZATION PROBLEMS; ORIGINAL ALGORITHMS; PROJECTION ALGORITHMS; TOTAL VARIATION;

ALGORITHMS; COMPUTATIONAL EFFICIENCY; FUNCTIONS; IMAGE RECONSTRUCTION; OPTIMIZATION; PROBLEM SOLVING; SET THEORY;

ITERATIVE METHODS;

EID: 77954036226     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/26/6/065008     Document Type: Article

References (35)

1. Aharoni R and Censor Y 1989 Block-iterative projection methods for parallel computation of solutions to convex feasibility problems Linear Algebra Appl. 120 165-75
2. Bauschke H H and Borwein J M 1996 On projection algorithms for solving convex feasibility problems SIAM Rev. 38 367-426
3. Bauschke H H, Combettes P L and Kruk S G 2006 Extrapolation algorithm for affine-convex feasibility problems Numer. Algorithms 41 239-74
4. Bauschke H H, Matoukov E and Reich S 2004 Projection and proximal point methods: convergence results and counterexamples Nonlinear Anal. 56 715-38
5. Butnariu D and Censor Y 1990 On the behavior of a block-iterative projection method for solving convex feasibility problems Int. J. Comput. Math. 34 79-94
6. Butnariu D, Davidi R, Herman G T and Kazantsev I G 2007 Stable convergence behavior under summable perturbations of a class of projection methods for convex feasibility and optimization problems IEEE J. Sel. Top. Sign. Process. 1 540-7
7. Butnariu D, Reich S and Zaslavski A J 2006 Convergence to fixed points of inexact orbits of Bregman-monotone and nonexpansive operators in Banach spaces Fixed Point Theory and Applications ed H F Nathansky, B G de Buen, K Goebel, W A Kirk and B Sims (Yokohama: Yokohama Publishers) pp 11-32
8. Butnariu D, Reich S and Zaslavski A J 2008 Stable convergence theorems for infinite products and powers of nonexpansive mappings Numer. Funct. Anal. Opt. 29 304-23
9. Byrne C L 2008 Applied Iterative Methods (Wellesley, MA, USA: AK Peters)
10. Censor Y, Chen W, Combettes P L, Davidi R and Herman G T 2009 On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints Optimization Online http://www.optimization-online.org/ DB-HTML/2009/12/2500.html
11. Censor Y, Elfving T and Herman G T 2001 Averaging strings of sequential iterations for convex feasibility problems Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications ed D Butnariu, Y Censor and S Reich (Amsterdam: Elsevier) pp 101-14
12. Censor Y, Elfving T, Kopf N and Bortfeld T 2005 The multiple-sets split feasibility problem and its applications for inverse problems Inverse Problems 21 2071-84
13. Censor Y, Gordon D and Gordon R 2001 BICAV: a block-iterative, parallel algorithm for sparse systems with pixel-related weighting IEEE Trans. Med. Imaging 20 1050-60
14. Censor Y and Segal A 2009 On the string averaging method for sparse common fixed points problems Int. Trans. Oper. Res. 16 481-94
15. Censor Y and Tom E 2003 Convergence of string-averaging projection schemes for inconsistent convex feasibility problems Optim. Methods Softw. 18 543-54
16. Censor Y and Zenios S A 1997 Parallel Optimization: Theory, Algorithms and Applications (New York: Oxford University Press)
17. Chinneck J W 2007 Feasibility and Infeasibility in Optimization: Algorithms and Computational Methods (New York: Springer)
18. Combettes P L 1996 The convex feasibility problem in image recovery Adv. Imag. Elec. Phys. 95 155-270
19. Combettes P L 1997 Hilbertian convex feasibility problem: convergence of projection methods Appl. Math. Opt. 35 311-30
20. Combettes P L 1997 Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections IEEE Trans. Image Process. 6 493-506
21. Combettes P L and Luo J 2002 An adaptive level set method for nondifferentiable constrained image recovery IEEE Trans. Image Process. 11 1295-304
22. Crombez G 2002 Finding common fixed points of strict paracontractions by averaging strings of sequential iterations J. Nonlinear Convex Anal. 3 345-51
23. Davidi R, Herman G T and Censor Y 2009 Perturbation-resilient block-iterative projection methods with application to image reconstruction from projections Int. Trans. Oper. Res. 16 505-24
24. Davidi R, Herman G T and Klukowska J 2009 SNARK09: a programming system for the reconstruction of 2D images from 1D projections http://www.snark09.com/
25. Eggermont P P B, Herman G T and Lent A 1981 Iterative algorithms for large partitioned linear systems, with applications to image reconstruction Linear Algebra Appl. 40 37-67
26. Gonzlez-Castão F J, García-Palomares U M, Alba-Castro J L and Pousada Carballo J M 2001 Fast image recovery using dynamic load balancing in parallel architectures, by means of incomplete projections IEEE Trans. Image Process. 10 493-99
27. Herman G T 2009 Fundamentals of Computerized Tomography: Image Reconstruction from Projections 2nd edn (London: Springer)
28. Herman G T and Davidi R 2008 On image reconstruction from a small number of projections Inverse Problems 24 045011
29. Kiwiel K C and Łopuch B 1997 Surrogate projection methods for finding fixed points of firmly nonexpansive mappings SIAM J. Optim. 7 1084-102
30. Ottavy N 1988 Strong convergence of projection-like methods in Hilbert spaces J. Optim. Theory Appl. 56 433-61
31. Penfold S N, Schulte R W, Censor Y, Bashkirov V, McAllister S, Schubert K E and Rosenfeld A B 2010 Block-iterative and string-averaging projection algorithms in proton computed tomography image reconstruction Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems ed Y Censor, M Jiang and G Wang (Madison, WI, USA: Medical Physics Publishing)
32. Pierra G 1984 Decomposition through formalization in a product space Math. Program. 28 96-115
33. Rhee H 2003 An application of the string averaging method to one-sided best simultaneous approximation J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 10 49-56
34. Schöpfer F, Schuster T and Louis A K 2008 An iterative regularization method for the solution of the split feasibility problem in Banach spaces Inverse Problems 24 055008
35. Zhao J and Yang Q 2005 Several solution methods for the split feasibility problem Inverse Problems 21 1791-9