Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

[1] H.H. Bauschke and J.M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Review 38 (1996), 367-426.10.1137/S0036144593251710Search in Google Scholar

[2] H.H. Bauschke and V.R. Koch, Projection methods: Swiss army knives for solving feasibility and best approximation problems with half-spaces, Contemporary Mathematics, 636, pp. 1-40, (2015).<https://people.ok.ubc.ca/bauschke/Research/c16.pdf>.Search in Google Scholar

[3] D. Butnariu, R. Davidi, G.T. Herman, and I.G. Kazantsev, Stable convergence behavior under summable perturbations of a class of projection methods for convex feasibility and optimization problems, IEEE Journal of Selected Topics in Signal Processing 1 (2007), 540-547.10.1109/JSTSP.2007.910263Search in Google Scholar

[4] D. Butnariu, S. Reich and A.J. Zaslavski, Convergence to fixed points of inexact orbits of Bregman-monotone and of nonexpansive operators in Banach spaces, in: H.F. Nathansky, B.G. de Buen, K. Goebel, W.A. Kirk, and B. Sims, Fixed Point Theory and its Applications, (Conference Proceedings, Guanajuato, Mexico, 2005), Yokahama Publishers, Yokahama, Japan, pp. 11-32, 2006.Search in Google Scholar

[5] D. Butnariu, S. Reich and A.J. Zaslavski, Stable convergence theorems for infinite products and powers of nonexpansive mappings, Numerical Functional Analysis and Optimization 29 (2008), 304{323.10.1080/01630560801998161Search in Google Scholar

[6] Y. Censor and A. Cegielski, Projection methods: an annotated bibliography of books and reviews, Optimization, accepted for publication. DOI:10.1080/02331934.2014.957701.10.1080/02331934.2014.957701Search in Google Scholar

[7] Y. Censor, W. Chen, P.L. Combettes, R. Davidi and G.T. Herman, On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints, Computational Optimization and Applications 51 (2012), 1065-1088.10.1007/s10589-011-9401-7Search in Google Scholar

[8] Y. Censor, R. Davidi and G.T. Herman, Perturbation resilience and superiorization of iterative algorithms, Inverse Problems 26 (2010), 065008 (12pp).10.1088/0266-5611/26/6/065008Search in Google Scholar

[9] Y. Censor, T. Elfving and G.T. Herman, Averaging strings of sequential iterations for convex feasibility problems. In: D. Butnariu, Y. Censor and S. Reich (editors), Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, Elsevier Science Publishers, Amsterdam, 2001, pp. 101-114.10.1016/S1570-579X(01)80009-4Search in Google Scholar

[10] Y. Censor, R. Davidi, G.T. Herman, R.W. Schulte and L. Tetruashvili, Projected subgradient minimization versus superiorization, Journal of Optimization Theory and Applications 160 (2014), 730-747.10.1007/s10957-013-0408-3Search in Google Scholar

[11] Y. Censor and D. Reem, Zero-convex functions, perturbation resilience, and subgradient projections for feasibility-seeking methods, Mathematical Programming, Series A, accepted.Search in Google Scholar

[12] Y. Censor and A. Segal, On the string averaging method for sparse common fixed point problems, International Transactions in Operational Research 16 (2009), 481{494.10.1111/j.1475-3995.2008.00684.x283925220300484Search in Google Scholar

[13] Y. Censor and A. Segal, On string-averaging for sparse problems and on the split common fixed point problem, Contemporary Mathematics 513 (2010), 125-142.10.1090/conm/513/10079Search in Google Scholar

[14] Y. Censor and E. Tom, Convergence of string-averaging projection schemes for inconsistent convex feasibility problems, Optimization Methods and Software 18 (2003), 543-554.10.1080/10556780310001610484Search in Google Scholar

[15] Y. Censor and A.J. Zaslavski, Convergence and perturbation resilience of dynamic string-averaging projection methods, Computational Optimization and Applications 54 (2013), 65-76.10.1007/s10589-012-9491-xSearch in Google Scholar

[16] Y. Censor and A.J. Zaslavski, String-averaging projected subgradient methods for constrained minimization, Optimization Methods & Software 29 (2014), 658-670.10.1080/10556788.2013.841693Search in Google Scholar

[17] Y. Censor and A.J. Zaslavski, Strict Fejér monotonicity by superiorization of feasibility-seeking projection methods, Journal of Optimization Theory and Applications, 165, 172-187, (2015). DOI:10.1007/s10957-014-0591-x.10.1007/s10957-014-0591-xSearch in Google Scholar

[18] P.L. Combettes, On the numerical robustness of the parallel projection method in signal synthesis, IEEE Signal Processing Letters 8 (2001), 45{47.10.1109/97.895371Search in Google Scholar

[19] G. Crombez, Finding common fixed points of strict paracontractions by averaging strings of sequential iterations, Journal of Nonlinear and Convex Analysis 3 (2002), 345-351.Search in Google Scholar

[20] R. Davidi, Algorithms for Superiorization and their Applications to Image Reconstruction, Ph.D. dissertation, Department of Computer Science, The City University of New York, NY, USA, 2010.Search in Google Scholar

[21] R. Davidi, G.T. Herman, and Y. Censor, Perturbation-resilient block-iterative projection methods with application to image reconstruction from projections, International Transactions in Operational Research 16 (2009), 505-524.10.1111/j.1475-3995.2009.00695.x352993923271857Search in Google Scholar

[22] R. Davidi, Y. Censor, R.W. Schulte, S. Geneser and L. Xing, Feasibilityseeking and superiorization algorithms applied to inverse treatment planning in radiation therapy, Contemporary Mathematics, 636, 83-92, (2015).<http://math.haifa.ac.il/yair/con-math-DCSGX-_nal-300114.pdf>Search in Google Scholar

[23] E. Garduño, and G.T. Herman, Superiorization of the ML-EM algorithm, IEEE Transactions on Nuclear Science 61 (2014), 162-172.10.1109/TNS.2013.2283529Search in Google Scholar

[24] D. Gordon and R. Gordon, Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems, SIAM Journal on Scientific Computing 27 (2005), 1092-1117.10.1137/040609458Search in Google Scholar

[25] G.T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, Springer-Verlag, London, UK, 2nd Edition, 2009.Search in Google Scholar

[26] G.T. Herman, Superiorization for image analysis, in: Combinatorial Image Analysis, Lecture Notes in Computer Science Vol. 8466, Springer, 2014, pp. 1-7. DOI: 10.1007/978-3-319-07148-0 1.10.1007/978-3-319-07148-0Search in Google Scholar

[27] G.T. Herman and R. Davidi, Image reconstruction from a small number of projections, Inverse Problems 24 (2008), 045011 (17pp).10.1088/0266-5611/24/4/045011277604119911080Search in Google Scholar

[28] G.T. Herman, E. Garduño, R. Davidi and Y. Censor, Superiorization: An optimization heuristic for medical physics, Medical Physics 39 (2012), 5532-5546.10.1118/1.474556622957620Search in Google Scholar

[29] W. Jin, Y. Censor and M. Jiang, A heuristic superiorization-like approach to bioluminescence, International Federation for Medical and Biological Engineering (IFMBE) Proceedings 39 (2013), 1026{1029.10.1007/978-3-642-29305-4_269Search in Google Scholar

[30] S. Luo and T. Zhou, Superiorization of EM algorithm and its application in single-photon emission computed tomography (SPECT), Inverse Problems and Imaging 8 (2014), 223{246.10.3934/ipi.2014.8.223Search in Google Scholar

[31] T. Nikazad, R. Davidi and G.T. Herman, Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction, Inverse Problems 28 (2012), 035005 (19pp).10.1088/0266-5611/28/3/035005357964823440911Search in Google Scholar

[32] S.N. Penfold, R.W. Schulte, Y. Censor, V. Bashkirov, S. McAllister, K.E. Schubert and A.B. Rosenfeld, Block-iterative and string-averaging projection algorithms in proton computed tomography image reconstruction. In: Y. Censor, M. Jiang and G. Wang (editors), Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Medical Physics Publishing, Madison, WI, USA, 2010, pp. 347-367.Search in Google Scholar

[33] S.N. Penfold, R.W. Schulte, Y. Censor and A.B. Rosenfeld, Total variation superiorization schemes in proton computed tomography image reconstruction, Medical Physics 37 (2010), 5887-5895.10.1118/1.3504603298054721158301Search in Google Scholar

[34] H. Rhee, An application of the string averaging method to one-sided best simultaneous approximation, Journal of the Korean Society of Mathematical Education, Series B, Pure and Applied Mathematics 10 (2003), 49-56.Search in Google Scholar

[35] M.J. Schrapp and G.T. Herman, Data fusion in X-ray computed tomography using a superiorization approach, Review of Scientific Instruments 85 (2014), 053701 (9pp).10.1063/1.487237824880376Search in Google Scholar