Superiorization

Superiorization and Perturbation Resilience of Algorithms: A Bibliography

compiled and continuously updated by Yair Censor

This page (at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html) is a, chronologically ordered, bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms, compiled and continuously updated by Yair Censor. If you know of a related work in any form (preprint, reprint, journal publication, conference report, abstract or poster, book chapter, thesis, etc.) that should be included here kindly write to me on: yair@math.haifa.ac.il with full bibliographic details, a DOI if available, and a PDF copy of the work if possible. Copyright notice: Downloads are supplied for personal academic use only. A download is considered equivalent to a pre-print or re-print request. Use is granted consistent with fair-use of a pre-print or re-print. By downloading any of the following materials you are agreeing to these terms.

 

This page was initiated on March 7, 2015, and has been last updated on March 24, 2017.

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Trailer:

The superiorization methodology works by taking an iterative algorithm, investigating its perturbation resilience, and then using proactively such perturbations in order to "force" the perturbed algorithm to do in addition to its original task something useful. 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 by steering its iterates according to the perturbations.

This is a very general principle, which has been successfully used in some important practical applications 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 a feasibility-seeking algorithm, or one that strives to find constraint-compatible points for a family of constraints, and the perturbations that are interlaced into the original algorithm aim at reducing (not necessarily minimizing) a given merit function.

To a novice on the superiorization methodology and perturbation resilience of algorithms we recommend to read first the recent reviews in [25] and [39] below.

For a recent detailed description of previous work that is related to superiorization but is not included in this bibliography we direct the reader to Section 3 of [24] below.

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 appears only inside the work [23, Subsection 6.2.1: Optimization vs. Superiorization].

 

 

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. [Abstract].

[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, R. Davidi and G.T. Herman, 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). http://www.marshallplan.at/images/papers_ scholarship/2014/Salzburg_University_of_Applied_Sciences_LangthalerOliver_2014.pdf. [Abstract].

[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). http://www.marshallplan.at/images/papers_ scholarship/2014/Salzburg_University_of_Applied_Sciences_PrommeggerBernhard_2014.pdf. [Abstract].

[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. [Abstract].

[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]   T. Humphries, J. Winn and A. Faridani, Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data, arXiv:1608.03931, (2017). [arXiv:1608.03931]. [Abstract].

[49]   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.

[50]   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].

[51]   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].

[52]    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].

[53]    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].

[54]   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].

[55]   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.

[56]   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].

[57]   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].

[58]   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].

[59]   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].

[60]   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].

[61]   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].

[62]   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].

[63]   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].

[64]   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].

[65]   C. Bargetz, S. Reich and R. Zalas, Convergence properties of dynamic string averaging projection methods in the presence of perturbations, arXiv:1703.07803, accepted for publication in Numerical Algorithms, (2017). [arXiv:1703.07803]. [Abstract].

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!

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