Superiorization

Superiorization and Perturbation Resilience of Algorithms: A Bibliography

compiled and continuously updated by Yair Censor

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Trailer:

We replace the text that appeared in this trailer in the previous versions of the page with a quotation of three paragraphs from the preface to the special issue: Y. Censor, G.T. Herman and M. Jiang (Guest Editors), "Superiorization: Theory and Applications", Special Issue of the journal Inverse Problems, Volume 33, Number 4, April 2017 [50] (all references refer to the bibliography below), followed by some additional notes.

"The superiorization methodology is used for improving the efficacy of iterative algorithms whose convergence is resilient to certain kinds of perturbations. Such perturbations are designed to 'force' the perturbed algorithm to produce more useful results for the intended application than the ones that are produced by the original iterative algorithm. The perturbed algorithm is called the 'superiorized version' of the original unperturbed algorithm. If the original algorithm is computationally efficient and useful in terms of the application at hand and if the perturbations are simple and not expensive to calculate, then the advantage of this method is that, for essentially the computational cost of the original algorithm, we are able to get something more desirable by steering its iterates according to the designed perturbations. This is a very general principle that has been used successfully in some important practical applications, especially for inverse problems such as image reconstruction from projections, intensity-modulated radiation therapy and nondestructive testing, and awaits to be implemented and tested in additional fields.

An important case is when the original algorithm is 'feasibility-seeking' (in the sense that it strives to find some point that is compatible with a family of constraints) and the perturbations that are introduced into the original iterative algorithm aim at reducing (not necessarily minimizing) a given merit function. In this case superiorization has a unique place in optimization theory and practice. Many constrained optimization methods are based on methods for unconstrained optimization that are adapted to deal with constraints. Such is, for example, the class of projected gradient methods wherein the unconstrained minimization inner step 'leads' the process and a projection onto the whole constraint set (the feasible set) is performed after each minimization step in order to regain feasibility. This projection onto the constraints set is in itself a non-trivial optimization problem and the need to solve it in every iteration hinders projected gradient methods and limits their efficiency only to feasible sets that are 'simple to project onto.' Barrier or penalty methods likewise are based on unconstrained optimization combined with various 'add-on's that guarantee that the constraints are preserved. Regularization methods embed the constraints into a 'regularized' objecive function and proceed with unconstrained solution methods for the new regularized objective function.

In contrast to these approaches, the superiorization methodology can be viewed as an antipodal way of thinking. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce merit function values. This is done while retaining the feasibility-seeking nature of the algorithm and without paying a high computational price. Furthermore, general-purpose approaches have been developed for automatically superiorizing iterative algorithms for large classes of constraints sets and merit functions; these provide algorithms for many application tasks." (end of qoute.)

To a novice on the superiorization methodology and perturbation resilience of algorithms we recommend to read first the recent reviews in [16, 25, 39]. For a recent description of previous work that is related to superiorization but is not included here, such as the works of Sidky and Pan, e.g., [6], we direct the reader to [24, section 3]. The SNARK14 software package [42], with its in-built capability to superiorize iterative algorithms to improve their performance, can be helpful to practitioners. Naturally there is variability among the bibliography items below in their degree of relevance to the superiorization methodology and perturbation resilience of algorithms. In some, such as in, e.g., [23] below, superiorization does not appear in the title, abstract or introduction but only inside the work, e.g., [23, Subsection 6.2.1: Optimization vs. Superiorization].

A word about the history. The terms and notions "superiorization" and "perturbation resilience" first appeared in the 2009 paper of Davidi, Herman and Censor [7] which followed its 2007 forerunner by Butnariu, Davidi, Herman and Kazantsev [3]. The ideas have some of their roots in the 2006 and 2008 papers of Butnariu, Reich and Zaslavski [2, 4]. All these culminated in Ran Davidi's 2010 Ph.D. dissertation [13].

The Bibliography:

[1]   P.L. Combettes, On the numerical robustness of the parallel projection method in signal synthesis, IEEE Signal Processing Letters, Vol. 8, pp. 45-47, (2001). DOI:10.1109/97.895371. [Abstract].

[2]   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 (Editors), Fixed Point Theory and its Applications, (Conference Proceedings, Guanajuato, Mexico, 2005), Yokahama Publishers, Yokahama, Japan, pp. 11-32, 2006. http://www.ybook.co.jp/pub/ISBN%20978-4-9465525-0.htm. [Abstract].

[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, Vol. 1, pp. 540-547, (2007). DOI:10.1109/JSTSP.2007.910263. [Abstract].

[4]   D. Butnariu, S. Reich and A.J. Zaslavski, Stable convergence theorems for infinite products and powers of nonexpansive mappings, Numerical Functional Analysis and Optimization, Vol. 29, pp. 304-323, (2008). DOI:10.1080/01630560801998161. [Abstract].

[5]   G.T. Herman and R. Davidi, Image reconstruction from a small number of projections, Inverse Problems, Vol. 24, 045011 (17pp), (2008). DOI:10.1088/0266-5611/24/4/045011. [Abstract].

[6]   E.Y. Sidky and X. Pan, Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization, Physics in Medicine and Biology, Vol. 53,  pp. 4777-4807, (2008). DOI:10.1088/0031-9155/53/17/021. [Abstract].

[7]   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, Vol. 16, pp. 505-524, (2009). DOI:10.1111/j.1475-3995.2009.00695.x. Final version preprint PDF (624KB) file. E-reprint of published paper available upon request.

[8]   G.T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, Springer-Verlag, London, UK, 2nd Edition, 2009. DOI:10.1007/978-1-84628-723-7.

[9]   S.N. Penfold, Image Reconstruction and Monte Carlo Simulations in the Development of Proton Computed Tomography for Applications in Proton Radiation Therapy, Ph.D. dissertation, Centre for Medical Radiation Physics, University of Wollongong, 2010. http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4305&context=theses

[10]   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. Final version preprint PDF (463KB) file. E-reprint of published paper available upon request. https://www.medicalphysics.org/SimpleCMS.php?content=reviewlist.php&isbn=9781930524484.

[11]   Y. Censor, R. Davidi and G.T. Herman, Perturbation resilience and superiorization of iterative algorithms, Inverse Problems, Vol. 26, (2010) 065008 (12pp). DOI:10.1088/0266-5611/26/6/065008. Final version preprint PDF (394KB) file. E-reprint of published paper available upon request.

[12]   S.N. Penfold, R.W. Schulte, Y. Censor and A.B. Rosenfeld, Total variation superiorization schemes in proton computed tomography image reconstruction, Medical Physics, Vol. 37, pp. 5887-5895, (2010). DOI:10.1118/1.3504603. Final version preprint PDF (339KB) file. E-reprint of published paper available upon request.

[13]   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. http://gradworks.umi.com/34/26/3426727.html. [Abstract].

[14]   E. Garduño, G.T. Herman and R. Davidi, Reconstruction from a few projections by ℓ1-minimization of the Haar transform, Inverse Problems, Vol. 27, 055006, (2011). DOI:10.1088/0266-5611/27/5/055006. [Abstract].

[15]   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, Vol. 51, pp. 1065-1088, (2012). DOI:10.1007/s10589-011-9401-7. Final version preprint PDF (721KB) file. E-reprint of published paper available upon request. A related (unpublished) Technical Report: W. Chen, Data sets of very large linear feasibility problems solved by projection methods, March 2, 2011, can be viewed here: PDF (66KB).

[16]   G.T. Herman, E. Garduño, R. Davidi and Y. Censor, Superiorization: An optimization heuristic for medical physics, Medical Physics, Vol. 39, pp. 5532-5546, (2012). DOI:10.1118/1.4745566. Final version preprint PDF (1,193KB) file. E-reprint of published paper available upon request.

[17]   R. Davidi, R.W. Schulte, Y. Censor and L. Xing, Fast superiorization using a dual perturbation scheme for proton computed tomography, Transactions of the American Nuclear Society, Vol. 106, pp. 73-76, (2012). Final version preprint PDF (591KB) file. E-reprint of published paper available upon request.

[18]   T. Nikazad, R. Davidi and G.T. Herman, Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction, Inverse Problems, Vol. 28, 035005 (19pp), (2012). DOI:10.1088/0266-5611/28/3/035005. [Abstract].

[19]   D. Steinberg, V. Bashkirov, V. Feng, R.F. Hurley, R.P. Johnson, S. Macafee, T. Plautz, H.F.-W. Sadrozinski, R. Schulte and A. Zatserklyaniy, Monte Carlo simulations for the development a clinical proton CT scanner, Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2012 IEEE, pp. 1311-1315. Oct. 27-Nov. 3, 2012, Anaheim, CA, USA. DOI:10.1109/NSSMIC.2012.6551320. [Abstract].

[20]   W. Jin, Y. Censor and M. Jiang, A heuristic superiorization-like approach to bioluminescence, International Federation for Medical and Biological Engineering (IFMBE) Proceedings, Vol. 39, pp. 1026-1029, (2013). DOI:10.1007/978-3-642-29305-4_269. Final version preprint PDF (297KB) file. E-reprint of published paper available upon request.

[21]   Y. Censor and A.J. Zaslavski, Convergence and perturbation resilience of dynamic string-averaging projection methods, Computational Optimization and Applications, Vol. 54, pp. 65-76, (2013). DOI:10.1007/s10589-012-9491-x. Final version preprint PDF (209KB) file. E-reprint of published paper available upon request.

[22]   S.-S. Luo, Reconstruction Algorithms for Single-photon Emission Computed Tomography, Ph.D. dissertation, Computational Mathematics, Peking University (PKU), Beijing, P.R. China, 2013. http://www.dissertationtopic.net/doc/2220625. [Abstract].

[23]   X. Zhang, Prior-Knowledge-Based Optimization Approaches for CT Metal Artifact Reduction, Ph.D. dissertation, Dept. of Electrical Engineering, Stanford University, Stanford, CA, USA, 2013. http://purl.stanford.edu/ws303zb5770. [Abstract].

[24]   Y. Censor, R. Davidi, G.T. Herman, R.W. Schulte and L. Tetruashvili, Projected subgradient minimization versus superiorization, Journal of Optimization Theory and Applications, Vol. 160, pp. 730-747, (2014). DOI:10.1007/s10957-013-0408-3. Final version preprint PDF (480KB) file. E-reprint of published paper available upon request.

[25]   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. [Abstract].

[26]   S. Luo and T. Zhou, Superiorization of EM algorithm and its application in single-photon emission computed tomography (SPECT), Inverse Problems and Imaging, Vol. 8, pp. 223-246, (2014). DOI:10.3934/ipi.2014.8.223. [Abstract].

[27]   M.J. Schrapp and G.T. Herman, Data fusion in X-ray computed tomography using a superiorization approach, Review of Scientific Instruments, Vol. 85, 053701 (9pp), (2014). DOI:10.1063/1.4872378. [Abstract].

[28]   M. Schrapp, M. Goldammer, K. Schörner and J. Stephan, Improvement of image quality in computed tomography via data fusion, Proceedings of the 5th International Conference on Industrial Computed Tomography (iCT), pp. 283-289, February 2014, the University of Applied Sciences, Wels, Upper Austria. http://www.ndt.net/article/ctc2014/papers/283.pdf. [Abstract].

[29]   E. Garduño and G.T. Herman, Superiorization of the ML-EM algorithm, IEEE Transactions on Nuclear Science, Vol. 61, pp. 162-172, (2014). DOI:10.1109/TNS.2013.2283529. [Abstract].

[30]   O. Langthaler, Incorporation of the Superiorization Methodology into Biomedical Imaging Software, Marshall Plan Scholarship Report, Salzburg University of Applied Sciences, Salzburg, Austria, and The Graduate Center of the City University of New York, NY, USA, September 2014, (76 pages).

[31]   B. Prommegger, Verification and Evaluation of Superiorized Algorithms Used in Biomedical Imaging: Comparison of Iterative Algorithms With and Without Superiorization for Image Reconstruction from Projections, Marshall Plan Scholarship Report, Salzburg University of Applied Sciences, Salzburg, Austria, and The Graduate Center of the City University of New York, NY, USA, October 2014, (84 pages).

[32]   D.C. Hansen, Improving Ion Computed Tomography, Ph.D. dissertation, Aarhus University, Experimental Clinical Oncology, Aarhus, Denmark, 2014. http://pure.au.dk//portal/files/83515131/dissertation.pdf. [Abstract].

[33]   J. Lee, C. Kim, B. Min, J. Kwak, S. Park, S-B. Lee, S. Park and S. Cho, Sparse-view proton computed tomography using modulated proton beams, Medical Physics, Vol. 42, pp. 1129-1137, (2015). DOI:10.1118/1.4906133. [Abstract].

[34]   T. Nikazad and M. Abbasi, Perturbation-resilient iterative methods with an infinite pool of mappings, SIAM Journal on Numerical Analysis, Vol. 53, pp. 390-404, (2015). DOI:10.1137/14095724X. [Abstract].

[35]   F. Arroyo, E. Arroyo, X. Li and J. Zhu, The convergence of the block cyclic projection with an overrelaxation parameter for compressed sensing based tomography, Journal of Computational and Applied Mathematics, Vol. 280, pp. 59-67, (2015). DOI:10.1016/j.cam.2014.11.036. [Abstract].

[36]   R. Davidi, Y. Censor, R.W. Schulte, S. Geneser and L. Xing, Feasibility-seeking and superiorization algorithms applied to inverse treatment planning in radiation therapy, Contemporary Mathematics, Vol. 636, pp. 83-92, (2015). DOI:10.1090/conm/636/12729. Final version preprint PDF (454KB) file. E-reprint of published paper available upon request.

[37]   Y. Censor and D. Reem, Zero-convex functions, perturbation resilience, and subgradient projections for feasibility-seeking methods, Mathematical Programming, Series A, Vol. 152, pp. 339-380, (2015). DOI:10.1007/s10107-014-0788-7. Final version preprint PDF (589KB) file. E-reprint of published paper available upon request.

[38]   Y. Censor and A.J. Zaslavski, Strict Fejér monotonicity by superiorization of feasibility-seeking projection methods, Journal of Optimization Theory and Applications, Vol. 165, pp. 172-187, (2015). DOI:10.1007/s10957-014-0591-x. Final version preprint PDF (216KB) file. E-reprint of published paper available upon request.

[39]   Y. Censor, Weak and strong superiorization: Between feasibility-seeking and minimization, Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, Vol. 23, pp. 41-54, (2015). DOI:10.1515/auom-2015-0046. Final version preprint PDF (213KB) file. E-reprint of published paper available upon request.

[40]   H.H. Bauschke and V.R. Koch, Projection methods: Swiss army knives for solving feasibility and best approximation problems with half-spaces, Contemporary Mathematics, Vol. 636, pp. 1-40, (2015). DOI:10.1090/conm/636/12726. https://people.ok.ubc.ca/bauschke/Research/c16.pdf. [Abstract].

[41]   M.J. Schrapp, Multi Modal Data Fusion in Industrial X-ray Computed Tomography, Ph.D. dissertation, Fakultät für Physik der Technischen Universität München, Munich, Germany, 2015.

[42]   SNARK14, A programming system for the reconstruction of 2D images from 1D projections designed to help researchers in developing and evaluating reconstruction algorithms. In particular, SNARK14 can be used for automatic superiorization of any iterative reconstruction algorithm. Released: 2015. Go to SNARK14.

[43]   W. Jin, Y. Censor and M. Jiang, Bounded perturbation resilience of projected scaled gradient methods, Computational Optimization and Applications, Vol. 63, pp. 365-392, (2016). DOI:10.1007/s10589-015-9777-x. Final version preprint PDF (357KB) file. E-reprint of published paper available upon request.

[44]   Q-L. Dong, J. Zhao and S. He, Bounded perturbation resilience of the viscosity algorithm, Journal of Inequalities and Applications, 2016:299 (12pp), 2016. DOI:10.1186/s13660-016-1242-6. [Abstract].

[45]   E. Nurminski, Finite-value superiorization for variational inequality problems, arXiv:1611.09697, (2016). [arXiv:1611.09697]. [Abstract].

[46]   S. Luo, Y. Zhang, T. Zhou and J. Song, Superiorized iteration based on proximal point method and its application to XCT image reconstruction, arXiv:1608.03931, (2016). [arXiv:1608.03931]. [Abstract].

[47]   Y. Censor and Y. Zur, Linear superiorization for infeasible linear programming, in: Y. Kochetov, M. Khachay, V. Beresnev, E. Nurminski and P. Pardalos (Editors), Discrete Optimization and Operations Research, Lecture Notes in Computer Science (LNCS), Vol. 9869, (2016), Springer International Publishing, pp. 15-24. DOI:10.1007/978-3-319-44914-2_2. [Abstract]. Reprint of the paper is available for free download on the publisher's website, under the link: "Download Sample pages 2 PDF (774.4 KB)" thereon.

[48]   C. Havas, Revised Implementation and Empirical Study of Maximum Likelihood Expectation Maximization Algorithms with and without Superiorization in Image Reconstruction, Marshall Plan Scholarship Report, Salzburg University of Applied Sciences, Salzburg, Austria, and The Graduate Center of the City University of New York, NY, USA, October 2016, (49 pages).

[49]   T. Humphries, J. Winn and A. Faridani, Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data, Physics in Medicine and Biology, Vol. 62 (2017), 6762. https://doi.org/10.1088/1361-6560/aa7c2d. [Abstract].

[50]   Y. Censor, G.T. Herman and M. Jiang, Guest Editors, Superiorization: Theory and Applications, Special Issue of the journal Inverse Problems, Volume 33, Number 4, April 2017. Read the Preface to the special issue on the journal's website, or here Preface. Read the titles and abstracts of all 14 papers included in the special issue on the journal's website at: titles and abstracts or consult items [51]-[64] below.

[51]   D. Reem and A. De Pierro, A new convergence analysis and perturbation resilience of some accelerated proximal forward-backward algorithms with errors, Inverse Problems, Vol. 33 (2017), 044001. https://doi.org/10.1088/1361-6420/33/4/044001. [Abstract].

[52]   T. Nikazad and M. Abbasi, A unified treatment of some perturbed fixed point iterative methods with an infinite pool of operators, Inverse Problems, Vol. 33 (2017), 044002. https://doi.org/10.1088/1361-6420/33/4/044002. [Abstract].

[53]    M. Yamagishi and I. Yamada, Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization, Inverse Problems, Vol. 33 (2017), 044003. https://doi.org/10.1088/1361-6420/33/4/044003. [Abstract].

[54]    A.J. Zaslavski, Asymptotic behavior of two algorithms for solving common fixed point problems, Inverse Problems, Vol. 33 (2017), 044004. https://doi.org/10.1088/1361-6420/33/4/044004. [Abstract].

[55]   S. Reich and A.J. Zaslavski, Convergence to approximate solutions and perturbation resilience of iterative algorithms, Inverse Problems, Vol. 33 (2017), 044005. https://doi.org/10.1088/1361-6420/33/4/044005. [Abstract].

[56]   Y. Censor, Can linear superiorization be useful for linear optimization problems? Inverse Problems, Vol. 33 (2017), 044006 (22pp). https://doi.org/10.1088/1361-6420/33/4/044006. [Abstract]. E-reprint of published paper available upon request.

[57]   H. He and H-K. Xu, Perturbation resilience and superiorization methodology of averaged mappings, Inverse Problems, Vol. 33 (2017), 044007. https://doi.org/10.1088/1361-6420/33/4/044007. [Abstract].

[58]   H-K. Xu, Bounded perturbation resilience and superiorization techniques for the projected scaled gradient method, Inverse Problems, Vol. 33 (2017), 044008. https://doi.org/10.1088/1361-6420/33/4/044008. [Abstract].

[59]   A. Cegielski and F. Al-Musallam, Superiorization with level control, Inverse Problems, Vol. 33 (2017), 044009. https://doi.org/10.1088/1361-6420/aa5d79. [Abstract].

[60]   E.S. Helou, M.V.W. Zibetti and E.X. Miqueles, Superiorization of incremental optimization algorithms for statistical tomographic image reconstruction, Inverse Problems, Vol. 33 (2017), 044010. https://doi.org/10.1088/1361-6420/33/4/044010. [Abstract].

[61]   E. Garduño and G.T. Herman, Computerized tomography with total variation and with shearlets, Inverse Problems, Vol. 33 (2017), 044011. https://doi.org/10.1088/1361-6420/33/4/044011. [Abstract].

[62]   E. Bonacker, A. Gibali, K-H. Küfer and P. Süss, Speedup of lexicographic optimization by superiorization and its applications to cancer radiotherapy treatment, Inverse Problems, Vol. 33 (2017), 044012. https://doi.org/10.1088/1361-6420/33/4/044012. [Abstract].

[63]   J. Zhu and S. Penfold, Total variation superiorization in dual-energy CT reconstruction for proton therapy treatment planning, Inverse Problems, Vol. 33 (2017), 044013. https://doi.org/10.1088/1361-6420/33/4/044013. [Abstract].

[64]   Q. Yang, W. Cong and G. Wang, Superiorization-based multi-energy CT image reconstruction, Inverse Problems, Vol. 33 (2017), 044014. https://doi.org/10.1088/1361-6420/aa5e0a. [Abstract].

[65]   T. Nikazad, M. Abbasi and T. Elfving, Error minimizing relaxation strategies in Landweber and Kaczmarz type iterations, Journal of Inverse and Ill-posed Problems, Vol. 25, pp. 35-56, (2017). DOI:10.1515/jiip-2015-0082. [Abstract].

[66]   Q.L. Dong, Y.J. Cho and Th.M. Rassias, Multi-step inertial Krasnosel'ski-Mann algorithm for nonexpansive operators, [Preprint from ResearchGate] (2017).

[67]   C.O.S. Sorzano, J. Vargas, J. Otón, J.M. de la Rosa-Trevín, J.L. Vilas, M. Kazemi, R. Melero, L. del Caño, J. Cuenca, P. Conesa, J. Gómez-Blanco, R. Marabini and J.M. Carazo, A survey of the use of iterative reconstruction algorithms in electron microscopy, BioMed Research International, Vol. 2017 (2017), Article ID 6482567, 17 pages, https://doi.org/10.1155/2017/6482567. [Free download of full paper from the publisher at hindawi.com]. Also [here, 1,413KB].

[68]   C.L. Byrne, The Dykstra and Bregman-Dykstra algorithms as superiorization (December 26, 2017). Technical report, (2017). [Preprint from ResearchGate].

[69]   Q.-L. Dong, A. Gibali, D. Jiang and S.-H. Ke, Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery, Fixed Point Theory and Applications, accepted for publication, (2017). [Preprint from arXiv].

[70]   Q.-L. Dong, A. Gibali, D. Jiang and Y.-C. Tang, Bounded perturbation resilience of extragradient-type methods and their applications, Journal of Inequalities and Applications, (2017) 2017:280. DOI:10.1186/s13660-017-1555-0. [Free download of full paper from the publisher].

[71]   A. Gibali and S. Petra, DC-programming versus ℓ0-superiorization for discrete tomography, Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, Vol. 26, pp. 105-133, (2018). Available at the journal's homepage here.

[72]   Yanni Guo, W. Cui and Yansha Guo, Perturbation resilience of proximal gradient algorithm for composite objectives, Journal of Nonlinear Sciences and Applications (JNSA), Vol. 10, pp. 5566-5575, (2017), http://dx.doi.org/10.22436/jnsa.010.10.36. [Free download of full paper from the publisher at http://www.isr-publications.com/jnsa]. Also [here, 693KB].

[73]   C. Bargetz, S. Reich and R. Zalas, Convergence properties of dynamic string averaging projection methods in the presence of perturbations, Numerical Algorithms, Vol. 77, pp. 185-209, (2018). https://doi.org/10.1007/s11075-017-0310-4. [Abstract].

[74]   M.V.W. Zibetti, C. Lin and G.T. Herman, Total variation superiorized conjugate gradient method for image reconstruction, Inverse Problems, Vol. 34 (2018), 034001. https://doi.org/10.1088/1361-6420/aaa49b. [Preprint from arXiv]. Marcelo V.W. Zibetti, Chuan Lin and Gabor T. Herman, Erratum: Total variation superiorized conjugate gradient method for image reconstruction (2018 Inverse Problems 34 034001), Inverse Problems, Vol. 36 (2020), 089601. https://doi.org/10.1088/1361-6420/ab9448.

[75]   A. Gibali, K-H. Küfer, D. Reem and P. Süss, A generalized projection-based scheme for solving convex constrained optimization problems, Computational Optimization and Applications, Vol. 70, pp. 737-762, (2018). https://doi.org/10.1007/s10589-018-9991-4. Reprint available on: Springer Nature SharedIt.

[76]   B. Schultze, Y. Censor, P. Karbasi, K.E. Schubert, and R.W. Schulte, An improved method of total variation superiorization applied to reconstruction in proton computed tomography, IEEE Transactions on Medical Imaging, accepted for publication. (2019). DOI:10.1109/TMI.2019.2911482. Final preprint PDF (2,002KB) and Supplemental materials PDF (574KB). Available on arXiv at: https://arxiv.org/abs/1803.01112. Available on IEEE Xplore Digital Library at: https://ieeexplore.ieee.org/document/8692608.

[77]   Y. Censor, H. Heaton, and R.W. Schulte, Derivative-free superiorization with component-wise perturbations. Numerical Algorithms, Vol. 80, pp. 1219-1240, (2019). https://doi.org/10.1007/s11075-018-0524-0. Preprint PDF (695KB) file. Available on arXiv at: https://arxiv.org/abs/1804.00123. Reprint available on: Springer Nature SharedIt.

[78]   Y. Guo and W. Cui, Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm, Journal of Inequalities and Applications, 2018:103, (2018), https://doi.org/10.1186/s13660-018-1695-x. [Free download of full paper from the publisher].

[79]   A.J. Zaslavski, Algorithms for Solving Common Fixed Point Problems, Springer International Publishing AG, part of Springer Nature, (2018). [Preface]. Freely available from the publisher at: https://link.springer.com/book/ 10.1007%2F978-3-319-77437-4.

[80]   T.Y. Kong, H. Pajoohesh and G.T. Herman, String-averaging algorithms for convex feasibility with infinitely many sets, Inverse Problems 35 (2019) 045011 (37pp). https://doi.org/10.1088/1361-6420/ab066c. [Preprint from arXiv].

[81]   T. Nikazad and M. Abbasi, Perturbed fixed point iterative methods based on pattern structure, Mathematical Methods in the Applied Sciences, (2018), 1-11. https://doi.org/10.1002/mma.5100. [Free download of full paper from the publisher].

[82]   E.S. Helou, G.T. Herman, C. Lin and M.V.W. Zibetti, Superiorization of preconditioned conjugate gradient algorithms for tomographic image reconstruction, Applied Analysis and Optimization, Vol. 2, pp. 271-284, (2018). Readable on Yokohama Publishers webpage.

[83]   Shousheng Luo, Yanchun Zhang, Tie Zhou, Jinping Song and Yanfei Wang, XCT image reconstruction by a modified superiorized iteration and theoretical analysis, Optimization Methods and Software, Vol. 35, pp. 1080-1097, (2020). Readable at https://doi.org/10.1080/10556788.2018.1560442.

[84]   P. Duan, X. Zheng and J. Zhao, Strong convergence theorems of viscosity iterative algorithms for split common fixed point problems, Mathematics, 2019, 7(1), 14;(2019). Open access at https://www.mdpi.com/2227-7390/7/1/14/htm.

[85]   Q.L. Dong, J. Huang, X.H. Li, Y.J. Cho and Th.M. Rassias, MiKM: multi-step inertial Krasnosel'skiĭ-Mann algorithm and its applications, Journal of Global Optimization, Vol. 73, pp. 801-824, (2019). https://link.springer.com/article/10.1007%2Fs10898-018-0727-x.

[86]   R. Davidi, R.M. Haralick and G.T. Herman, Derivative-free superiorization using the facet model, a presentation at the Seminar on Image Processing and Computer Vision, September 16, 2010. The Graduate Center, City University of New York (CUNY) (2010). PDF (243KB). A note from the page maintainer: In spite of this document being from 2010, I place it here because it came to my attention only very recently. y.c.

[87]   M.A. Kalkhoran and D. Vray, Sparse sampling and reconstruction for an optoacoustic ultrasound volumetric hand-held probe, Biomedical Optics Express, Vol. 10, pp. 1545-1556, (2019). Accessible at OSA Publishing webpage.

[88]   T. Humphries, PSARTSUP: a GitHub archive that contains code used for the Superiorized pSART method described in: "Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data" by Humphries, Winn and Faridani here, see item [49] above, and in: "Superiorized polyenergetic reconstruction algorithm for reduction of metal artifacts in CT images" by Humphries and Gibali here, see item [89] below. Released under the GNU Public License: https://www.gnu.org/licenses/gpl-3.0.en.html. Link to the PSARTSUP GitHub archive. (2017). A note from the page maintainer: In spite of this document being from 2017, I place it here because it came to my attention only very recently. y.c.

[89]   A. Gibali and T. Humphries, Superiorized polyenergetic reconstruction algorithm for reduction of metal artifacts in CT images. Proceedings of the 2017 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC 2017), October 21-28, 2017 Atlanta, Georgia, USA, pp. 920-925. (2017). See Proceedings table of contents. A note from the page maintainer: In spite of this document being from 2017, I place it here because it came to my attention only very recently. y.c.

[90]   G.T. Herman, Iterative reconstruction techniques and their superiorization for the inversion of the Radon transform, in: R. Ramlau and O. Scherzer, eds., The Radon Transform: The First 100 Years and Beyond, Chapter 10, pp. 217-238 (2019), De Gruyter, Berlin, Boston. https://doi.org/10.1515/9783110560855-010. See Book record on publisher's Website.

[91]   R. Cassetta, P. Piersimoni, M. Riboldi, V. Giacometti, V. Bashkirov, G. Baroni, C. Ordonez, G. Coutrakon and R. Schulte, Accuracy of low-dose proton CT image registration for pretreatment alignment verification in reference to planning proton CT, Journal of Applied Clinical Medical Physics, (2019);20:4:83-90. Available as open access at American Association of Physicists in Medicine. https://doi.org/10.1002/acm2.12565.

[92]   J. Fink, R.L.G. Cavalcante and S. Stanczak, Multicast Beamforming Using Semidefinite Relaxation and Bounded Perturbation Resilience, 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), (2019). Available as open access at IEEE Xplore Digital Library. DOI:10.1109/ICASSP.2019.8682325.

[93]   M. Hoseini, Superiorization and its importance in the optimization, ICNS Conference Proceeding, Vol. 3. Issue 2, pp. 6-9. (2019). Available at Charmo University, Kurdistan Region-Iraq. http://dx.doi.org/10.31530/17030.

[94]   E. Bonacker, A. Gibali and K.-H. Küfer, Accelerating Two Projection Methods via Perturbations with Application to Intensity-Modulated Radiation Therapy, Applied Mathematics & Optimization, (2019), accepted for publication. https://doi.org/10.1007/s00245-019-09571-4. Reprint readable on: Springer Nature SharedIt.

[95]   C.L. Byrne, Thoughts on superiorization. This is a sequence of five short preprints posted on ResearchGate between April 28 and June 21, 2019. A combined PDF is Here.

[96]   J. Fink, D. Schaeufele, M. Kasparick, R.L.G. Cavalcante and S. Stanczak, Cooperative Localization by Set-theoretic Estimation, WSA 2019; 23rd International ITG Workshop on Smart Antennas, pp. 1-8. WSA 2019, April 24-26, 2019, Vienna, Austria. (2019). Open access at: IEEE Xplore Digital Library.

[97]   S. Reich and R. Zalas, A modular string averaging procedure for solving the common fixed point problem for quasi-nonexpansive mappings in Hilbert space, Numerical Algorithms, Vol. 72, pp. 297-323, (2016). https://doi.org/10.1007/s11075-015-0045-z. Reprint readable on: Springer Nature SharedIt. A note from the page maintainer: Bounded perturbation resilience appears in Example 4.7. y.c.

[98]   Yanni Guo and Xiaozhi Zhao, Bounded Perturbation Resilience and Superiorization of Proximal Scaled Gradient Algorithm with Multi-Parameters, Mathematics, 7(6), 535 (14 pp) (2019). https://doi.org/10.3390/math7060535. Open access at: Scholarly open access publishing, MDPI.

[99]   S. Rai, Image Quality Measures in Proton Computed Tomography, M.Sc. (Master of Science) Thesis, Department of Physics, Northern Illinois University (NIU), De Kalb, IL, USA. (110 pp) (2015). https://commons.lib.niu.edu/handle/10843/18827. Available at: Northern Illinois University's digital repository .

[100]   Y. Censor, E. Garduño, E.S. Helou and G.T. Herman, Derivative-Free Superiorization: Principle and Algorithm, Numerical Algorithms, Vol. 88, pp. 227-248, (2021). https://doi.org/10.1007/s11075-020-01038-w. [Springer link: Online first].

[101]   Y. Censor, E. Levy, An analysis of the superiorization method via the principle of concentration of measure, Applied Mathematics and Optimization, accepted for publication (2019). https://arxiv.org/abs/1909.00398. [Preprint from arXiv].

[102]   C.L. Byrne, What do simulations tell us about superiorization? Preprint posted on ResearchGate. September 2019.

[103]   E. Bonacker, Perturbed Projection Methods in Convex Optimization - Applied to Radiotherapy Planning, Ph.D. Dissertation, Fachbereich Mathematik der Technischen Universität Kaiserslautern, Kaiserslautern, Germany. July 2019. Abstract, 75KB, PDF. Online Access Fulltext.

[104]   Peichao Duan and Xubang Zheng, Bounded perturbation resilience and superiorization techniques for a modified proximal gradient method, Optimization. (2019). [Reprint from https://www.tandfonline.com/doi/full/10.1080/02331934.2019.1686631].

[105]   Mohsen Hoseini, Shahram Saeidi and Do Sang Kim, On perturbed hybrid steepest descent method with minimization or superiorization for subdifferentiable functions, Numerical Algorithms, Vol. 85, pp. 353-374, (2020). https://doi.org/10.1007/s11075-019-00818-3. Reprint readable on: Springer Nature SharedIt.

[106]   Yamin Wang, Fenghui Wang and Haixia Zhang, Strong convergence of viscosity forward-backward algorithm to the sum of two accretive operators in Banach space, Optimization, (2019). https://doi.org/10.1080/02331934.2019.1705299. Full access at: https://www.tandfonline.com/.

[107]   Yanni Guo and Xiaozhi Zhao, Strong convergence of over-relaxed multiparameter proximal scaled gradient algorithm and superiorization, Optimization, (2020). https://doi.org/10.1080/02331934.2020.1722124. Full access at: https://www.tandfonline.com/.

[108]   Nuttapol Pakkaranang, Poom Kumam, Vasile Berinde and Yusuf I. Suleiman, Superiorization methodology and perturbation resilience of inertial proximal gradient algorithm with application to signal recovery, The Journal of Supercomputing, (2020). https://doi.org/10.1007/s11227-020-03215-z. Reprint readable on: SpringerLink.

[109]   Thomas Humphries and Boyang (Jessie) Wang, Superiorized method for metal artifact reduction. Medical Physics, Vol. 47, pp. 3984-3995 (2020). Published on line at: https://aapm.onlinelibrary.wiley.com/doi/abs/10.1002/mp.14332. [Preprint from arXiv].

[110]   Eliahu Levy, Accumulated Random Distances in High Dimensions-Ways of Calculation. Preprint. (2020). https://arxiv.org/abs/2003.10941. [Preprint from arXiv].

[111]   D.R. Sahu, Luoyi Shi, Ngai-Ching Wong and Jen-Chih Yao, Perturbed iterative methods for a general family of operators: convergence theory and applications, Optimization, (2020). https://doi.org/10.1080/02331934.2020.1745798. Full access at: https://www.tandfonline.com/.

[112]   Esther Bonacker, Aviv Gibali and Karl-Heinz Küfer, Nesterov perturbations and projection methods applied to IMRT, Journal of Nonlinear and Variational Analysis, Volume 4, Issue 1, Pages 63-86, 2020. Available online at [http://jnva.biemdas.com]. https://doi.org/10.23952/jnva.4.2020.1.06.

[113]   A. Gibali, G.T. Herman and C. Schnörr, Guest Editors, Superiorization versus Constrained Optimization: Analysis and Applications, Special Issue of Journal of Applied and Numerical Optimization (JANO), Volume 2, Number 1, April 2020. Read the special issue on the journal's website at: http: //jano.biemdas.com/archives/category/volume-2-issue-1.

[114]   A. Gibali, G.T. Herman and C. Schnörr, Editorial: A special issue focused on superiorization versus constrained optimization: analysis and applications, Journal of Applied and Numerical Optimization (JANO), Vol. 2, pp. 1-2, 2020. Read it on the journal's website at: http://jano.biemdas.com/issues/JANO2020-1-1-1.pdf.

[115]   Mokhtar Abbasi and Touraj Nikazad, Superiorization of block accelerated cyclic subgradient methods, Journal of Applied and Numerical Optimization (JANO), Vol. 2, pp. 3-13, 2020. Read it on the journal's website at: http://jano.biemdas.com/issues/JANO2020-1-2.pdf.

[116]   Y. Censor, S. Petra and C. Schnörr, Superiorization vs. accelerated convex optimization: The superiorized / regularized least-squares case, Journal of Applied and Numerical Optimization (JANO), Vol. 2, pp. 15-62, 2020. Read it on the journal's website at: http://jano.biemdas.com/issues/JANO2020-1-3.pdf.

[117]   A. Gibali and M. Haltmeier, Superiorized regularization of inverse problems, Journal of Applied and Numerical Optimization (JANO), Vol. 2, pp. 63-70, 2020. Read it on the journal's website at: http://jano.biemdas.com/issues/JANO2020-1-4.pdf.

[118]   Gabor T. Herman, Problem structures in the theory and practice of superiorization, Journal of Applied and Numerical Optimization (JANO), Vol. 2, pp. 71-76, 2020. Read it on the journal's website at: http://jano.biemdas.com/issues/JANO2020-1-5.pdf.

[119]   T. Humphries, M. Loreto, B. Halter, W. O'Keeffe and L. Ramirez, Comparison of regularized and superiorized methods for tomographic image reconstruction, Journal of Applied and Numerical Optimization (JANO), Vol. 2, pp. 77-99, 2020. Read it on the journal's website at: http://jano.biemdas.com/issues/JANO2020-1-6.pdf.

[120]   S. Reich and A.J. Zaslavski, Inexact orbits of set-valued nonexpansive mappings with summable errors, Journal of Applied and Numerical Optimization (JANO), Vol. 2, pp. 101-107, 2020. Read it on the journal's website at: http://jano.biemdas.com/issues/JANO2020-1-7.pdf.

[121]   A.J. Zaslavski, Three extensions of Butnariu-Reich-Zaslavski theorem for inexact infinite products of nonexpansive mappings, Journal of Applied and Numerical Optimization (JANO), Vol. 2, pp. 109-120, 2020. Read it on the journal's website at: http://jano.biemdas.com/issues/JANO2020-1-8.pdf.

[122]   Satoshi Takabe and Tadashi Wadayama, Deep unfolded multicast beamforming. Preprint. (2020). https://arxiv.org/pdf/2004.09345.pdf. [Preprint from arXiv]. (This work is related to [92] above).

[123]   Elias S. Helou, Marcelo V. W. Zibetti and Gabor T. Herman, Fast Proximal Gradient Methods for Nonsmooth Convex Optimization for Tomographic Image Reconstruction, Sensing and Imaging, accepted for publication. (2020). https://arxiv.org/abs/2008.09720. [Preprint from arXiv].

[124]   Nikolai Janakiev, Superiorized Algorithms for Medical Image Processing: Comparison of Shearlet-based Secondary Optimization Criteria, Marshall Plan Scholarship Report, Salzburg University of Applied Sciences, Salzburg, Austria, and The Graduate Center of the City University of New York, NY, USA, September 2016, (63 pages).

[125]   Lukas Kiefer, Stefania Petra, Martin Storath and Andreas Weinmann, Multi-channel Potts-based reconstruction for multi-spectral computed tomography, Preprint (2020). https://arxiv.org/abs/2009.05814. [Preprint from arXiv].

[126]   Johan Alme, Gergely Gábor Barnaföldi, Rene Barthel, Vyacheslav Borshchov, Tea Bodova, Anthony van den Brink, Stephan Brons, Mamdouh Chaar, Viljar Eikeland, Grigory Feofilov, Georgi Genov, Silje Grimstad, Ola Grøttvik, Håvard Helstrup, Alf Herland, Annar Eivindplass Hilde, Sergey Igolkin, Ralf Keidel, Chinorat Kobdaj, Naomi van der Kolk, Oleksandr Listratenko, Qasim Waheed Malik, Shruti Mehendale, Ilker Meric, Simon Voigt Nesbø, Odd Harald Odland, Gábor Papp, Thomas Peitzmann, Helge Egil Seime Pettersen, Pierluigi Piersimoni, Maksym Protsenko, Attiq Ur Rehman, Matthias Richter, Dieter Röhrich, Andreas Tefre Samnøy, Joao Seco, Lena Setterdahl, Hesam Shafiee, Øistein Jelmert Skjolddal, Emilie Solheim, Arnon Songmoolnak, Ákos Sudár, Jarle Rambo Sølie, Ganesh Tambave, Ihor Tymchuk, Kjetil Ullaland, Håkon Andreas Underdal, Monika Varga-Köfaragó, Lennart Volz, Boris Wagner, Fredrik Mekki Widerøe, RenZheng Xiao, Shiming Yang, Hiroki Yokoyama, A High-Granularity Digital Tracking Calorimeter Optimized for Proton CT, Frontiers in Physics, Vol. 8, article 568243, (20pp), (2020). DOI:10.3389/fphy.2020.568243. https://www.frontiersin.org/articles/10.3389/fphy.2020.568243/full [Open access].

[127]   Alexander J. Zaslavski, Nonsmooth Convex Optimization. In: Alexander J. Zaslavski, The Projected Subgradient Algorithm in Convex Optimization. SpringerBriefs in Optimization. Springer, Cham., pp. 5-83, 2020. Available from the publisher at https://doi.org/10.1007/978-3-030-60300-7_2.

[128]   Lukas Kiefer, Efficient Algorithms for Mumford-Shah and Potts Problems, Ph.D. Dissertation, Combined Faculty for the Natural Sciences and Mathematics, Heidelberg University, Germany. (220 pp.) (2020). DOI:https://doi.org/10.11588/heidok.00029100. Available at: heiDOK-The Heidelberg Document Repository.

[129]   Nuttapol Pakkaranang, Poom Kumam, Yusuf I. Suleiman and Bashir Ali, Bounded perturbation resilience of viscosity proximal algorithm for solving split variational inclusion problems with applications to compressed sensing and image recovery, Mathematical Methods in the Applied Sciences, pp. 1-23, 2020. The journal's website is at: https://onlinelibrary.wiley.com/doi/10.1002/mma.7023.

[130]   Peichao Duan and Xubang Zheng, Bounded perturbation resilience of generalized viscosity iterative algorithms for split variational inclusion problems, Applied Set-Valued Analysis and Optimization, Vol. 2, pp. 49-61, 2020. DOI:10.23952/asvao.2.2020.1.04. Open Access on the journal's website at: http://asvao.biemdas.com/archives/1051.

[131]   Jochen Fink, Renato L.G. Cavalcante and Slawomir Stanczak, Multi-group multicast beamforming by superiorized projections onto convex sets, IEEE Transactions on Signal Processing , Vol. 69, pp. 5708-5722, 2021. https://ieeexplore.ieee.org/document/9557796. IEEEXplore.

[132]   Idan Steinberg, Jeesu Kim, Martin K. Schneider, Dongwoon Hyun, Aimen Zlitni, Sarah M. Hooper, Tal Klap, Geoffrey A. Sonn, Jeremy J. Dahl, Chulhong Kim, Sanjiv Sam Gambhir, Superiorized Photo-Acoustic Non-NEgative Reconstruction (SPANNER) for Clinical Photoacoustic Imaging, IEEE Transactions on Medical Imaging, 2021. https://ieeexplore.ieee.org/document/9383259. [Open Access from the publisher at IEEEXplore]. DOI:10.1109/TMI.2021.3068181.

[133]   Sebastian Meyer, Marco Pinto, Katia Parodi and Chiara Gianoli, The impact of path estimates in iterative ion CT reconstructions for clinical-like cases, Physics in Medicine and Biology, accepted for publication, 2021. https://doi.org/10.1088/1361-6560/abf1ff.

[134]   Weizhe Han, Qianlong Wang and Weiwei Cai, Computed tomography imaging spectrometry based on superiorization and guided image filtering, Optics Letters, Vol. 46, pp. 2208-2211, 2021, https://doi.org/10.1364/OL.418355. [The Optical Society (OSA)].

[135]   Howard Heaton, Samy Wu Fung, Aviv Gibali and Wotao Yin, Feasibility-based Fixed Point Networks, 2021. https://arxiv.org/abs/2104.14090. [Preprint from arXiv].

[136]   Maria Guenter, Comparison of Algorithms for Solving the Least Squares Problem with Applications in Computed Tomography, Master of Science Thesis, Faculty of Science, Department of Computer Science, Mathematics, Physics and Statistics, The University of British Columbia (UBC), Okanagan, BC, Canada. (94 pp) (2021). https://open.library.ubc.ca/cIRcle/collections/ubctheses/24/items/1.0398196. Available at: UBC Library Open Collection .

[137]   Chongyuan Shui, Yihong Wang, Weiwei Cai, and Bin Zhou, Linear multispectral absorption tomography based on regularized iterative methods, Optics Express, Vol. 29, pp. 20889-20912, 2021, https://doi.org/10.1364/OE.421817. [Open Access from The Optical Society (OSA)].

[138]   Kaiwen Ma, Nikolaos V. Sahinidis, Sreekanth Rajagopalan, Satyajith Amaran and Scott J. Bury, Decomposition in derivative-free optimization, Journal of Global Optimization, Vol. 81, pp. 269-292, 2021. https://doi.org/10.1007/s10898-021-01051-w. Reprint readable on: Springer Nature SharedIt.

[139]   Mark Brooke, Incorporation of Biological Factors in Radiation Therapy Treatment Planning, Ph.D. Dissertation, Department of Oncology, Wolfson College, University of Oxford, UK. December 2020.

[140]   Yair Censor, Keith E. Schubert and Reinhard W. Schulte, Developments in mathematical algorithms and computational tools for proton CT and particle therapy treatment planning, IEEE Transactions on Radiation and Plasma Medical Sciences, accepted for publication, (2021). Preprint available here: PDF (11MB). DOI:10.1109/TRPMS.2021.3107322. Early Access on IEEEXplore.

[141]   Yingying Li and Yaxuan Zhang, Bounded perturbation resilience of two modified relaxed CQ algorithms for the multiple-sets split feasibility problem, Axioms, 10, 197, 2021 (22 pages). https://doi.org/10.3390/axioms10030197. Open Access on the journal's website at: https://www.mdpi.com/journal/axioms.

[142]   Blake Edward Schultze, Essential Elements of Proton Computed Tomography for Practical Applications, Ph.D. Dissertation, Department of Electrical and Computer Engineering, Baylor University, Waco, TX, USA. August 2021. Document Preview available at: ProQuest Dissertations Publishing. https://www.proquest.com/openview/367d3b74fc7014cd494de42c941e019f/1?cbl=18750&diss=y&pq-origsite=gscholar.

[143]   Christina M. Sarosiek, Clinical Applications and Feasibility of Proton CT and Proton Radiography, Ph.D. Dissertation, Department of Physics, Northern Illinois University, IL, USA. August 2021. Document Preview available at: ProQuest Dissertations Publishing. https://www.proquest.com/openview/1b242ab746c6f28ba66fc6098b7a7a82/1?pq-origsite=gscholar&cbl=18750&diss=y.

[144]   T. Nikazad, M. Abbasi, L. Afzalipour and T. Elfving, A new step size rule for the superiorization method and its application in computerized tomography, Numerical Algorithms, 2021. https://doi.org/10.1007/s11075-021-01229-z. Reprint readable on: Springer Nature SharedIt.

[145]   Jingyan Xu and Frédéric Noo, Convex optimization algorithms in medical image reconstruction – in the age of AI, Physics in Medicine & Biology, 2021. http://iopscience.iop.org/article/10.1088/1361-6560/ac3842. Publisher's Webpage: Institute of Physics and Engineering in Medicine.

[146]   Maria Guenter, Steve Collins, Andy Ogilvy, Warren Hare and Andrew Jirasek, Superiorization versus regularization: A comparison of algorithms for solving image reconstruction problems with applications in computed tomography, Medical Physics, accepted for publication, 2021. https://doi.org/10.1111/mp.15373. Journal's Webpage: Medical Physics.

[147]   Howard Wayne Heaton, Learning to Optimize with Guarantees, Ph.D. Dissertation, Department of Mathematics, University of California, Los Angeles, CA, USA. 2021. Dissertation available at: eScholarship Publishing. https://escholarship.org/content/qt3274t029/qt3274t029.pdf.

[148]   Ruiwen Xing, Thomas Humphries and Dong Si, Self-Attention Generative Adversarial Network for Iterative Reconstruction of CT Images, 2022. https://arxiv.org/abs/2112.12810. [Preprint from arXiv].

[149]   Qiao-Li Dong, Yeol Je Cho, Songnian He, Panos M. Pardalos and Themistocles M. Rassias, The inertial Krasnosel'skiĭ–Mann iteration, In: The Krasnosel'skiĭ–Mann Iterative Method: Recent Progress and Applications, SpringerBriefs in Optimization, Springer, Cham, Switzerland, Chapter 5 (pp.59-73), 2022. https://link.springer.com/chapter/10.1007/978-3-030-91654-1_5. Available on SpringerLink .

[150]   Jochen Fink, Renato L.G. Cavalcante and Slawomir Stanczak, Superiorized Adaptive Projected Subgradient Method with Application to MIMO Detection, 2022. https://arxiv.org/abs/2203.01116. [Preprint from arXiv].

[151]   Yair Censor, Daniel Reem and Maroun Zaknoon, A generalized block-iterative projection method for the common fixed point problem induced by cutters, Journal of Global Optimization, Vol. 84, pp. 967-987, (2022). DOI:https://link.springer.com/article/10.1007/s10898-022-01175-7. [Springer link: Online first]. Reprint on: Springer Nature SharedIt.

[152]   Jochen Fink, Renato L.G. Cavalcante, Zoran Utkovski, and Slawomir Stanczak, A Set-Theoretic Approach to Mimo Detection, in: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP-2022), 2022, pp. 5328-5332. DOI:10.1109/ICASSP43922.2022.9746548. Free access on IEEEXplore.

[153]   Idan Steinberg and Sanjiv Sam Gambhir (Inventors), Real-time photoacoustic imaging using a precise forward model and fast iterative inverse, Patent application number: 17/517401, Publication date: May 5, 2022. See: https://portal.uspto.gov/pair/PublicPair. The full application appears at the United States Patent and Trademark Office (USPTO). This is related to item [132] above on this webpage.

[154]   W. Cui, Research And Application Of Superiorization Algorithm For Convex Optimization Problems, Master Thesis, College of Science, Civil Aviation University of China, Tianjin, P.R. China. Posted on: February 17, 2021. Thesis abstract and table of contents available at: Global Thesis. https://www.globethesis.com/?t=2370330611468675.

[155]   Oriol García Llopis, Superiorización en Programación Lineal [English: Superiorization in Linear Programming], Bachelor Thesis, Department of Mathematics, Faculty of Science, University of Alicante, Alicante, Spain. Posted on: June 28, 2022. Thesis, in Spanish with English abstract, freely available at: RUA. Repositorio Institucional de la Universidad de Alicante. https://rua.ua.es/dspace/handle/10045/124555.

[156]   Mahdi Mirzapour and Hossein Rabbani, Investigation on accelerated ordered subsets image reconstruction techniques with superiorization methodology, The European Physical Journal Plus, Volume 137, Article number: 791, 2022. Reprint on: Springer Link. https://doi.org/10.1140/epjp/s13360-022-02964-5.

[157]   Francisco J. Aragón-Artacho, Yair Censor, Aviv Gibali and David Torregrosa-Belén, The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning, Applied Mathematics and Computation, Vol. 440, Article 127627 (2023). Open Access at: https://doi.org/10.1016/j.amc.2022.127627, or here: PDF (1,928KB).

[158]   Xiangyu Zeng, Shuhao Xia, Kai Yang, Youlong Wu and Yuanming Shi, Over-the-Air Computation for Vertical Federated Learning, in: 2022 IEEE International Conference on Communications Workshops (ICC Workshops), pp. 788-793, 2022. doi:10.1109/ICCWorkshops53468.2022.9814484. Link to: IEEEXplore.

[159]   Florian Barkmann, Yair Censor and Niklas Wahl, Superiorization as a novel strategy for linearly constrained inverse radiotherapy treatment planning, Preprint, July 26, 2022. Available on arXiv at: https://arxiv.org/abs/2207.13187, or here: PDF (1,148KB).

[160]   Yiran Jia, Noah McMichael, Pedro Mokarzel, Brandon Thompson, Dong Si and Thomas Humphries, Superiorization-inspired unrolled SART algorithm with U-Net generated perturbations for sparse-view and limited-angle CT reconstruction, Physics in Medicine & Biology, (2022). Online at: http://iopscience.iop.org/article/10.1088/1361-6560/aca513,

[161]   Alexander J. Zaslavski, Superiorization with a projected subgradient method, Journal of Applied and Numerical Optimization, Vol. 4, pp. 291-298.(2022). Online at: http://jano.biemdas.com/archives/1357.

[162]   Yair Censor, Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction, Applied Set-Valued Analysis and Optimization, accepted for publication, (2022). Available on Optimization Online at: https://optimization-online.org/?p=21478, on arXiv at: https://arxiv.org/abs/2212.14724, or here: PDF (440KB).

[163]   Müzeyyen Ertürk and Ahmet Salkim, Superiorization and bounded perturbation resilience of a gradient projection algorithm solving the convex minimization problem, Optimization Letters, (2023). DOI:https://doi.org/10.1007/s11590-022-01961-y. [Springer link: Online first]. Reprint on: Springer Nature SharedIt.

[164]   Yiji Wang, Cheng Zou, Dingzhu Wen and Yuanming Shi, Federated Learning over LEO Satellite, 2022 IEEE Globecom Workshops (GC Wkshps): Edge Learning over 5G Mobile Networks and Beyond, Rio de Janeiro, Brazil, (2022), pp. 1652-1657. DOI:10.1109/GCWkshps56602.2022.10008719. Reprint on: https://ieeexplore.ieee.org/abstract/document/10008719.

[165]   Alexander J. Zaslavski, Two Convergence Results for Inexact Infinite Products of Non-Expansive Mappings, Axioms, 12, 88 (2023), (9pp). DOI:https://doi.org/10.3390/axioms12010088. Open access at MDPI.com.

To view a PDF version of this page in a format of a Technical Report that is annualy updated go to arXiv at http://arxiv.org/abs/1506.04219. Original report: June 13, 2015 contained 41 items. First revision: March 9, 2017 contained 64 items. Second revision: March 8, 2018 contained 76 items. Third revision: March 11, 2019 contains 90 items. Fourth revision: March 16, 2020 contains 112 items. Fifth revision: March 18, 2021 contains 132 items. Sixth revision: March 13, 2022 contains 150 items.

Dear visitor, if you have written a paper related to Superiorization and Perturbation Resilience of Algorithms, or if you are aware of a paper on this topic which is not listed above, either published or in preprint form, please let me know so that I can add it and keep this list up to date. Thank you!

This page was initiated on March 7, 2015, and has been last updated on January 22, 2023.

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