IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v259y2015icp173-186.html
   My bibliography  Save this article

A convergent least-squares regularized blind deconvolution approach

Author

Listed:
  • Cornelio, Anastasia
  • Porta, Federica
  • Prato, Marco

Abstract

The aim of this work is to present a new and efficient optimization method for the solution of blind deconvolution problems with data corrupted by Gaussian noise, which can be reformulated as a constrained minimization problem whose unknowns are the point spread function (PSF) of the acquisition system and the true image. The objective function we consider is the weighted sum of the least-squares fit-to-data discrepancy and possible regularization terms accounting for specific features to be preserved in both the image and the PSF. The solution of the corresponding minimization problem is addressed by means of a proximal alternating linearized minimization (PALM) algorithm, in which the updating procedure is made up of one step of a gradient projection method along the arc and the choice of the parameter identifying the steplength in the descent direction is performed automatically by exploiting the optimality conditions of the problem. The resulting approach is a particular case of a general scheme whose convergence to stationary points of the constrained minimization problem has been recently proved. The effectiveness of the iterative method is validated in several numerical simulations in image reconstruction problems.

Suggested Citation

  • Cornelio, Anastasia & Porta, Federica & Prato, Marco, 2015. "A convergent least-squares regularized blind deconvolution approach," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 173-186.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:173-186
    DOI: 10.1016/j.amc.2015.02.048
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315002362
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.02.048?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    2. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    3. Paola Brianzi & Fabio Di Benedetto & Claudio Estatico, 2013. "Preconditioned iterative regularization in Banach spaces," Computational Optimization and Applications, Springer, vol. 54(2), pages 263-282, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bonettini, Silvia & Prato, Marco & Rebegoldi, Simone, 2016. "A cyclic block coordinate descent method with generalized gradient projections," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 288-300.
    2. S. Bonettini & M. Prato & S. Rebegoldi, 2018. "A block coordinate variable metric linesearch based proximal gradient method," Computational Optimization and Applications, Springer, vol. 71(1), pages 5-52, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Silvia Bonettini & Peter Ochs & Marco Prato & Simone Rebegoldi, 2023. "An abstract convergence framework with application to inertial inexact forward–backward methods," Computational Optimization and Applications, Springer, vol. 84(2), pages 319-362, March.
    2. S. Bonettini & M. Prato & S. Rebegoldi, 2018. "A block coordinate variable metric linesearch based proximal gradient method," Computational Optimization and Applications, Springer, vol. 71(1), pages 5-52, September.
    3. Bonettini, Silvia & Prato, Marco & Rebegoldi, Simone, 2016. "A cyclic block coordinate descent method with generalized gradient projections," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 288-300.
    4. Nguyen Hieu Thao, 2018. "A convergent relaxation of the Douglas–Rachford algorithm," Computational Optimization and Applications, Springer, vol. 70(3), pages 841-863, July.
    5. Jérôme Bolte & Edouard Pauwels, 2016. "Majorization-Minimization Procedures and Convergence of SQP Methods for Semi-Algebraic and Tame Programs," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 442-465, May.
    6. Bo Wen & Xiaojun Chen & Ting Kei Pong, 2018. "A proximal difference-of-convex algorithm with extrapolation," Computational Optimization and Applications, Springer, vol. 69(2), pages 297-324, March.
    7. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
    8. Perraudin, Nathanaël & Holighaus, Nicki & Søndergaard, Peter L. & Balazs, Peter, 2018. "Designing Gabor windows using convex optimization," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 266-287.
    9. Lorenzo Stella & Andreas Themelis & Panagiotis Patrinos, 2017. "Forward–backward quasi-Newton methods for nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 67(3), pages 443-487, July.
    10. Guillaume Sagnol & Edouard Pauwels, 2019. "An unexpected connection between Bayes A-optimal designs and the group lasso," Statistical Papers, Springer, vol. 60(2), pages 565-584, April.
    11. Ernest K. Ryu & Yanli Liu & Wotao Yin, 2019. "Douglas–Rachford splitting and ADMM for pathological convex optimization," Computational Optimization and Applications, Springer, vol. 74(3), pages 747-778, December.
    12. Junhong Lin & Lorenzo Rosasco & Silvia Villa & Ding-Xuan Zhou, 2018. "Modified Fejér sequences and applications," Computational Optimization and Applications, Springer, vol. 71(1), pages 95-113, September.
    13. Maryam Yashtini, 2022. "Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 913-939, December.
    14. Puya Latafat & Panagiotis Patrinos, 2017. "Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators," Computational Optimization and Applications, Springer, vol. 68(1), pages 57-93, September.
    15. Le Thi Khanh Hien & Duy Nhat Phan & Nicolas Gillis, 2022. "Inertial alternating direction method of multipliers for non-convex non-smooth optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 247-285, September.
    16. Sedi Bartz & Rubén Campoy & Hung M. Phan, 2022. "An Adaptive Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1019-1055, December.
    17. Francesco Rinaldi & Damiano Zeffiro, 2023. "Avoiding bad steps in Frank-Wolfe variants," Computational Optimization and Applications, Springer, vol. 84(1), pages 225-264, January.
    18. Emilie Chouzenoux & Jean-Christophe Pesquet & Audrey Repetti, 2016. "A block coordinate variable metric forward–backward algorithm," Journal of Global Optimization, Springer, vol. 66(3), pages 457-485, November.
    19. Hedy Attouch & Alexandre Cabot & Zaki Chbani & Hassan Riahi, 2018. "Inertial Forward–Backward Algorithms with Perturbations: Application to Tikhonov Regularization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 1-36, October.
    20. Kely D. V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 865-889, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:173-186. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.