Skip to main content
SpringerLink
Log in

Iterative regularization algorithms for constrained image deblurring on graphics processors

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

The ability of the modern graphics processors to operate on large matrices in parallel can be exploited for solving constrained image deblurring problems in a short time. In particular, in this paper we propose the parallel implementation of two iterative regularization methods: the well known expectation maximization algorithm and a recent scaled gradient projection method. The main differences between the considered approaches and their impact on the parallel implementations are discussed. The effectiveness of the parallel schemes and the speedups over standard CPU implementations are evaluated on test problems arising from astronomical images.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barzilai J., Borwein J.M.: Two point step size gradient methods. IMA J. Numer. Anal. 8, 141–148 (1988)

    Article  Google Scholar 

  2. Bertero M., Boccacci P.: Introduction to Inverse Problems in Imaging. Institute of Physics Publishing, Bristol (1998)

    Book  Google Scholar 

  3. Bonettini S., Zanella R., Zanni L.: A scaled gradient projection method for constrained image deblurring. Inverse Probl. 25, 015002 (2009)

    Article  Google Scholar 

  4. Csiszär I.: Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems. Ann. Stat. 19, 2032–2066 (1991)

    Article  Google Scholar 

  5. Dai Y.H., Fletcher R.: On the asymptotic behaviour of some new gradient methods. Math. Program. 103(3), 541–559 (2005)

    Article  Google Scholar 

  6. Dai Y.H., Hager W.W., Schittkowski K., Zhang H.: The cyclic barzilai-borwein method for unconstrained optimization. IMA J. Numer. Anal. 26, 604–627 (2006)

    Article  Google Scholar 

  7. Davis P.J.: Circulant Matrices. Wiley, New York (1979)

    Google Scholar 

  8. Frassoldati G., Zanghirati G., Zanni L.: New adaptive stepsize selections in gradient methods. J. Ind. Manag. Optim. 4(2), 299–312 (2008)

    Google Scholar 

  9. Friedlander A., Martínez J.M., Molina B., Raydan M.: Gradient method with retards and generalizations. SIAM J. Numer. Anal. 36, 275–289 (1999)

    Article  Google Scholar 

  10. Galligani E., Ruggiero V., Zanni L.: Parallel solution of large-scale quadratic programs. In: De Leone, R., Murli, A., Pardalos, P.M., Toraldo, G. (eds) High Performance Algorithms and Software in Nonlinear Optimization, Applied Optimization 24, pp. 189–205. Kluwer Academic Publ, Dordrecht (1998)

    Google Scholar 

  11. Gergel V.P., Sergeyev Y.D., Strongin R.G.: A parallel global optimization method and its implementation on a transputer system. Optimization 26, 261–275 (1992)

    Article  Google Scholar 

  12. Hansen P.C.: Rank-deficient and Discrete Ill-posed Problems. SIAM, Philadelphia (1998)

    Google Scholar 

  13. Harris, M.: Optimizing parallel reduction in CUDA. NVidia Technical Report (2007). Available: http://developer.download.nvidia.com/compute/cuda/1_1/Website/projects/reduction/doc/reduction.pdf

  14. Iusem A.N.: Convergence analysis for a multiplicatively relaxed EM algorithm. Math. Meth. Appl. Sci. 14, 573–593 (1991)

    Article  Google Scholar 

  15. Iusem A.N.: A short convergence proof of the EM algorithm for a specific Poisson model. REBRAPE 6, 57–67 (1992)

    Google Scholar 

  16. Lange K., Carson R.: EM reconstruction algorithms for emission and transmission tomography. J. Comput. Assist. Tomogr. 8, 306–316 (1984)

    Google Scholar 

  17. Lee, S., Wright, S.J.: Implementing algorithms for signal and image reconstruction on graphical processing units. Submitted (2008). Available: http://www.optimization-online.org/DB_HTML/2008/11/2131.html

  18. Lucy L.B.: An iterative technique for the rectification of observed distributions. Astronom. J. 79, 745–754 (1974)

    Article  Google Scholar 

  19. Migdalas A., Toraldo G., Kumar V.: Parallel computing in numerical optimization. Parallel Comput. 24(4), 373–551 (2003)

    Article  Google Scholar 

  20. Mülthei H.N., Schorr B.: On properties of the iterative maximum likelihood reconstruction method. Math. Meth. Appl. Sci. 11, 331–342 (1989)

    Article  Google Scholar 

  21. NVIDIA: NVIDIA CUDA Compute Unified Device Architecture, Programming guide. Version 2.0 (2008). Available at: http://developer.download.nvidia.com/compute/cuda/2_0/docs/NVIDIA_CUDA_Programming_Guide_2.0.pdf

  22. Resmerita E., Engl H.W., Iusem A.N.: The expectation-maximization algorithm for ill-posed integral equations: a convergence analysis. Inverse Probl. 23, 2575–2588 (2007)

    Article  Google Scholar 

  23. Richardson W.H.: Bayesian-based iterative method of image restoration. J. Opt. Soc. Amer. A 62, 55–59 (1972)

    Article  Google Scholar 

  24. Rudin L.I., Osher S., Fatemi E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)

    Article  Google Scholar 

  25. Serafini T., Zanghirati G., Zanni L.: Gradient projection methods for quadratic programs and applications in training support vector machines. Optim. Meth. Soft. 20(2–3), 353–378 (2005)

    Article  Google Scholar 

  26. Shepp L.A., Vardi Y.: Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging 1, 113–122 (1982)

    Article  Google Scholar 

  27. Strongin R.G., Sergeyev Y.D.: Global multidimensional optimization on parallel computer. Parallel Comput. 18, 1259–1273 (1992)

    Article  Google Scholar 

  28. Strongin R.G., Sergeyev Ya.D.: Global Optimization with Non-convex Constraints and Parallel Algorithms. Kluwer Academic Publ., Dordrecht (2000)

    Google Scholar 

  29. Vardi Y., Shepp L.A., Kaufman L.: A statistical model for positron emission tomography. J. Amer. Statist. Soc. 80(389), 8–37 (1985)

    Google Scholar 

  30. Zanella R., Boccacci P., Zanni L., Bertero M.: Efficient gradient projection methods for edge-preserving removal of Poisson noise. Inverse Probl. 25, 045010 (2009)

    Article  Google Scholar 

  31. Zanni L.: An improved gradient projection-based decomposition technique for support vector machines. Comput. Manag. Sci. 3, 131–145 (2006)

    Article  Google Scholar 

  32. Zanni L., Serafini T., Zanghirati G.: Parallel software for training large scale support vector machines on multiprocessor systems. J. Mach. Learn. Res. 7, 1467–1492 (2006)

    Google Scholar 

  33. Zhou B., Gao L., Dai Y.H.: Gradient methods with adaptive step-sizes. Comput. Optim. Appl. 35(1), 69–86 (2006)

    Article  Google Scholar 

  34. Zhu, M., Chan, T.F.: An efficient primal-dual hybrid gradient algorithm for total variation image restoration. CAM Report 08-34, Mathematics Department, UCLA (2008)

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Ferrara, Polo Scientifico Tecnologico, Blocco B, Via Saragat 1, 44100, Ferrara, Italy

    Valeria Ruggiero

  2. Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100, Modena, Italy

    Thomas Serafini, Riccardo Zanella & Luca Zanni

Authors
  1. Valeria Ruggiero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Serafini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Riccardo Zanella
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Luca Zanni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luca Zanni.

Additional information

This research is supported by the PRIN2006 project of the Italian Ministry of University and Research Inverse Problems in Medicine and Astronomy, grant 2006018748.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruggiero, V., Serafini, T., Zanella, R. et al. Iterative regularization algorithms for constrained image deblurring on graphics processors. J Glob Optim 48, 145–157 (2010). https://doi.org/10.1007/s10898-009-9516-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-009-9516-x

Keywords

Search

Navigation