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Alternative minimisation algorithm for non-local total variational image deblurring

Alternative minimisation algorithm for non-local total variational image deblurring

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Recently, variational models based on non-local regularisation obtain superior results over traditional methods, and many iterative algorithms have been proposed for these models. At present, Xiaoqun Zhang et al. proposed two algorithms based on Bregman iteration for solving non-local regularisation problems, these algorithms converge fast but the calculation quantity is large for each iterative step. Here, based on the idea of variable splitting and penalty techniques in optimisation and fast Fourier transform, the authors present a non-local total variational model and propose a fast iterative algorithm for the model. Under some assumption, q-linear convergence of the iterative algorithm is proved. Experiments demonstrate that the algorithm can efficiently speed up the execution of the variational model and obtain an improvement in signal-to-noise ratio through the selection of penalty parameters.

Inspec keywords: variational techniques; minimisation; image restoration; iterative methods; fast Fourier transforms

Other keywords: nonlocal total variational image deblurring; minimisation algorithm; fast Fourier transform; fast iterative algorithm; nonlocal regularisation; nonlocal total variational model; q-linear convergence; penalty technique; penalty parameter; variable splitting; Bregman iteration; signal-to-noise ratio

Subjects: Optical, image and video signal processing; Optimisation techniques; Computer vision and image processing techniques; Interpolation and function approximation (numerical analysis); Optimisation techniques; Integral transforms; Interpolation and function approximation (numerical analysis); Integral transforms

References

    1. 1)
      • T. Goldstein , S. Osher . The split bregman method for l1 regularized problems. SIAM J. Imag. Sci. , 2 , 323 - 343
    2. 2)
      • A. Buades , B. Coll , J.-M. Morel . On image denoising methods. SIAM Multiscale Model. Simul. , 2 , 490 - 530
    3. 3)
      • S. Osher , Y. Mao , B. Dong , W. Yin . Fast linearized Bregman iteration for compressive sensing and sparse denoising. Commun. Math. Sci. , 1 , 93 - 111
    4. 4)
      • J.-F. Cai , S. Osher , Z. Shen . Convergence of the linearized Bregman iteration for l1-norm minimization. Math. Comp. , 268 , 2127 - 2136
    5. 5)
      • Peyre, G., Bougleux, S., Cohen, L.: `Non-local regularization of inverse problems', Proc. 10th European Conf. on Computer Vision, October 2008, Marseille, France, p. 57–68.
    6. 6)
      • S. Osher , R. Fedkiw . (2002) Level set methods and dynamic implicit surfaces.
    7. 7)
      • G. Gilboa , S. Osher . Nonlocal operators with applications to image processing. Multiscale Model. Simul. , 3 , 1005 - 1028
    8. 8)
      • H.C. Andrews , B.R. Hunt . (1977) Digital image restoration.
    9. 9)
      • J. Yang , Y. Zhang , W. Yin . An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise. SIAM J. Scientific Comput. , 4 , 2842 - 2865
    10. 10)
      • I. Daubechies , G. Teschke , L. Vese . Iteratively solving linear inverse problems under general convex constraints. Inverse Probl. Imaging , 29 - 46
    11. 11)
      • J. Yang , W. Yin , Y. Zhang , Y. Wang . A fast algorithm for edgepreserving variational multichannel image restoration. SIAM J. Imag. Sci. , 2 , 569 - 592
    12. 12)
      • A.S. Carasso . Linear and nonlinear image deblurring: a documented study. SIAM J. Numer. Anal. , 6 , 1659 - 1689
    13. 13)
      • L. Rudin , S. Osher , E. Fatemi . Nonlinear total variation based noise removal algorithms. Phys. D , 259 - 268
    14. 14)
      • V. Kolmogorov , R. Zabih . What energy functions can be minimized via graph cuts?. IEEE Trans. Pattern Anal. Mach. Intell. , 2 , 147 - 159
    15. 15)
      • X. Zhang , M. Burger , X. Bresson , S. Osher . Bregmanized nonlocal regularization for deconvolution and sparse reconstruction.
    16. 16)
      • Y. Lou , X. Zhang , S. Osher , A. Bertozzi . Image recovery via nonlocal operators. J. Scientific Comput. , 2 , 185 - 197
    17. 17)
      • Rudin, L., Osher, S.: `Total variation based image restoration with free local constraints', Proc. First IEEE ICIP, 1994, Austin, USA, p. 31–35.
    18. 18)
      • E.T. Hale , W. Yin , Y. Zhang . Fixed-point continuation for l1-minimization: methodology and convergence. SIAM J. Optim. , 3 , 1107 - 1130
    19. 19)
      • Y. Wang , J. Yang , W. Yin , Y. Zhang . A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. , 3 , 248 - 272
    20. 20)
      • J.-F. Cai , S. Osher , Z. Shen . Linearized Bregman iterations for frame-based image deblurring. SIAM J. Imag. Sci. , 1 , 226 - 252
    21. 21)
      • A. Chambolle . An algorithm for total variation minimization and applications. J. Math. Im. Vis. , 89 - 97
    22. 22)
      • I. Ekeland , R. Temam . Convex analysis and variational problems. SIAM Classics Appl. Math. , 68 - 69
    23. 23)
      • J. Nocedal , S.J. Wright . (1999) Numerical optimization.
    24. 24)
      • A.N. Tikhonov , V.Y. Arsenin . Solution of ill-posed problems.
    25. 25)
      • Zhou, D., Scholkopf, B.: `Regularization on discrete spaces', Proc. 27th DAGM Symp. on Pattern Recognition, Vienna, September 2005, Austria, p. 361–368.
    26. 26)
      • S. Osher , M. Burger , D. Goldfarb , J. Xu , W. Yin . An iterative regularization method for total variation-based image restoration. SIAM Multiscale Model. Simul. , 460 - 489
    27. 27)
      • S. Durand , M. Nikolova . Denoising of frame coefficients using l1 data-fidelity term and edge preserving regularization. SIAM Multiscale Model. Simul. , 2 , 547 - 576
    28. 28)
      • G. Gilboa , S. Osher . Nonlocal linear image regularization and supervised segmentation. SIAM Multiscale Model. Simul. , 2 , 595 - 630
    29. 29)
      • S. Kindermann , S. Osher , P.W. Jones . Deblurring and denoising of images by nonlocal functional. SIAM Multiscale Model Simul. , 4 , 1091 - 1115
    30. 30)
      • W. Yin , S. Osher , D. Goldfarb , J. Darbon . Bregman iterative algoruithms for l1 minimization with applications to compressed sensing. SIAM J. Imaging Sci. , 143 - 168
    31. 31)
      • Bougleux, S., Elmoataz, A., Melkemi, M.: `Discrete regularization on weighted graphs for image and mesh filtering', First Int. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM 2007), May 2007, Ischia, Italy, p. 128–139.
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