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Volumn 5, Issue 2, 2011, Pages 511-530

Non-local regularization of inverse problems

Author keywords

Compressive sensing; Inpainting; Non local regularization; Super resolution

Indexed keywords


EID: 79957937908     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2011.5.511     Document Type: Article
Times cited : (99)

References (61)
  • 2
    • 67651033716 scopus 로고    scopus 로고
    • Some rst-order algorithms for total variation based image restoration
    • J.-F. Aujol, Some rst-order algorithms for total variation based image restoration, J. Math. Imaging Vis., 34 (2009), 307-327.
    • (2009) J. Math. Imaging Vis. , vol.34 , pp. 307-327
    • Aujol, J.-F.1
  • 6
    • 24644484251 scopus 로고    scopus 로고
    • 1-unied variational framework for image restoration
    • pages, Springer-Verlag
    • J. Bect, L. Blanc Féraud, G. Aubert and A. Chambolle, A l1-unied variational framework for image restoration, In "Proc. of ECCV04," pages Vol 4, 1-13. Springer-Verlag, 2004.
    • (2004) Proc. of ECCV04. , vol.4 , pp. 1-13
    • Bect, J.1    Blanc Féraud, L.2    Aubert, G.3    Chambolle, A.4
  • 9
    • 34948897097 scopus 로고    scopus 로고
    • Image enhancement by non-local reverse heat equation
    • A. Buades, B. Coll and J-M. Morel, "Image Enhancement By Non-local Reverse Heat Equation," Preprint CMLA 2006-22, 2006.
    • (2006) Preprint CMLA , pp. 2006-2022
    • Buades, A.1    Coll, B.2    Morel, J.-M.3
  • 11
    • 33947416035 scopus 로고    scopus 로고
    • Near-optimal signal recovery from random projections: Universal encoding strategies?
    • E. Candés and T. Tao, Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Transactions on Information Theory, 52 (2006), 5406-5425.
    • (2006) IEEE Transactions on Information Theory , vol.52 , pp. 5406-5425
    • Candés, E.1    Tao, T.2
  • 12
    • 1242352408 scopus 로고    scopus 로고
    • An algorithm for total variation minimization and applications
    • A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, 20 (2004), 89-97.
    • (2004) Journal of Mathematical Imaging and Vision , vol.20 , pp. 89-97
    • Chambolle, A.1
  • 13
    • 0036301838 scopus 로고    scopus 로고
    • Mathematical models for local nontexture inpaintings
    • T. Chan and J. Shen, Mathematical models for local nontexture inpaintings, SIAM J. Appl. Math, 62 (2002), 1019-1043.
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 1019-1043
    • Chan, T.1    Shen, J.2
  • 16
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forward-backward splitting
    • P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Modeling & Simulation, 4 (2005), 1168-1200.
    • (2005) Multiscale Modeling & Simulation , vol.4 , pp. 1168-1200
    • Combettes, P.L.1    Wajs, V.R.2
  • 17
  • 18
    • 34248586002 scopus 로고    scopus 로고
    • Example-based single image super-resolution: A global map approach with outlier rejection
    • D. Datsenko and M. Elad, Example-based single image super-resolution: A global map approach with outlier rejection, Journal of Mult. System and Sig. Proc., 18 (2007), 103-121.
    • (2007) Journal of Mult. System and Sig. Proc. , vol.18 , pp. 103-121
    • Datsenko, D.1    Elad, M.2
  • 19
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math., 57 (2004), 1413-1541.
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 1413-1541
    • Daubechies, I.1    Defrise, M.2    de Mol, C.3
  • 21
    • 0041958932 scopus 로고
    • Ideal spatial adaptation via wavelet shrinkage
    • D. Donoho and I. Johnstone, Ideal spatial adaptation via wavelet shrinkage, Biometrika, 81 (1994), 425-455.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.1    Johnstone, I.2
  • 23
    • 37849040146 scopus 로고    scopus 로고
    • Solving the inverse problem of image zooming using 'self examples'
    • M. Ebrahimi and E. R. Vrscay, Solving the inverse problem of image zooming using 'self examples', In "ICIAR07," pages 117-130, 2007.
    • (2007) ICIAR07 , pp. 117-130
    • Ebrahimi, M.1    Vrscay, E.R.2
  • 24
    • 0033285309 scopus 로고    scopus 로고
    • Texture synthesis by non-parametric sampling
    • IEEE Computer Society
    • A. A. Efros and T. K. Leung, Texture synthesis by non-parametric sampling, In "Proc. of ICCV '99," page 1033. IEEE Computer Society, 1999.
    • (1999) Proc. of ICCV '99. , pp. 1033
    • Efros, A.A.1    Leung, T.K.2
  • 25
    • 33751379736 scopus 로고    scopus 로고
    • Image denoising via sparse and redundant representations over learned dictionaries
    • M. Elad and M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries, IEEE Trans. on Image Processing, 15 (2006), 3736-3745.
    • (2006) IEEE Trans. on Image Processing. , vol.15 , pp. 3736-3745
    • Elad, M.1    Aharon, M.2
  • 27
    • 45949105032 scopus 로고    scopus 로고
    • Nonlocal discrete regularization on weighted graphs: A framework for image and manifold processing
    • A. Elmoataz, O. Lezoray and S. Bougleux, Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing, IEEE Tr. on Image Processing, 17 (2008), 1047-1060.
    • (2008) IEEE Tr. on Image Processing. , vol.17 , pp. 1047-1060
    • Elmoataz, A.1    Lezoray, O.2    Bougleux, S.3
  • 29
    • 60649102899 scopus 로고    scopus 로고
    • Inpainting and zooming using sparse representations
    • M. J. Fadili, J.-L. Starck and F. Murtagh, Inpainting and zooming using sparse representations, The Computer Journal, 52 (2009), 64-79.
    • (2009) The Computer Journal , vol.52 , pp. 64-79
    • Fadili, M.J.1    Starck, J.-L.2    Murtagh, F.3
  • 32
    • 58149480054 scopus 로고    scopus 로고
    • Nonlocal convex functionals for image regularization
    • G. Gilboa, J. Darbon, S. Osher and T. F. Chan, "Nonlocal convex functionals for image regularization," UCLA CAM Report 06-57, 2006.
    • (2006) UCLA CAM Report , pp. 06-57
    • Gilboa, G.1    Darbon, J.2    Osher, S.3    Chan, T.F.4
  • 33
    • 41549098470 scopus 로고    scopus 로고
    • Nonlocal linear image regularization and supervised segmentation
    • G. Gilboa and S. Osher, Nonlocal linear image regularization and supervised segmentation, SIAM Multiscale Modeling and Simulation, 6 (2007), 595-630.
    • (2007) SIAM Multiscale Modeling and Simulation , vol.6 , pp. 595-630
    • Gilboa, G.1    Osher, S.2
  • 34
    • 57049132103 scopus 로고    scopus 로고
    • Nonlocal operators with applications to image processing
    • G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, SIAM Multiscale Modeling & Simulation, 7 (2008), 1005-1028.
    • (2008) SIAM Multiscale Modeling & Simulation , vol.7 , pp. 1005-1028
    • Gilboa, G.1    Osher, S.2
  • 35
    • 33845467001 scopus 로고    scopus 로고
    • Deblurring and denoising of images by nonlocal functionals
    • S. Kindermann, S. Osher and P. W. Jones, Deblurring and denoising of images by nonlocal functionals, SIAM Mult. Model. and Simul., 4 (2005), 1091-1115.
    • (2005) SIAM Mult. Model. and Simul. , vol.4 , pp. 1091-1115
    • Kindermann, S.1    Osher, S.2    Jones, P.W.3
  • 36
    • 29144467969 scopus 로고    scopus 로고
    • Fast image and video denoising via nonlocal means of similar neighborhoods
    • M. Mahmoudi and G. Sapiro, Fast image and video denoising via nonlocal means of similar neighborhoods, IEEE Signal Processing Letters, 12 (2005), 839-842.
    • (2005) IEEE Signal Processing Letters , vol.12 , pp. 839-842
    • Mahmoudi, M.1    Sapiro, G.2
  • 37
    • 39149089704 scopus 로고    scopus 로고
    • Sparse representation for color image restoration
    • J. Mairal, M. Elad and G. Sapiro, Sparse representation for color image restoration, IEEE Trans. Image Proc., 17 (2008), 53-69.
    • (2008) IEEE Trans. Image Proc. , vol.17 , pp. 53-69
    • Mairal, J.1    Elad, M.2    Sapiro, G.3
  • 38
    • 0035733621 scopus 로고    scopus 로고
    • Edge direction preserving image zooming: A mathematical and numerical analysis
    • F. Malgouyres and F. Guichard, Edge direction preserving image zooming: A mathematical and numerical analysis, SIAM Journal on Numer. An., 39 (2001), 1-37.
    • (2001) SIAM Journal on Numer. An. , vol.39 , pp. 1-37
    • Malgouyres, F.1    Guichard, F.2
  • 40
    • 0036474805 scopus 로고    scopus 로고
    • Disocclusion: A variational approach using level lines
    • S. Masnou, Disocclusion: A variational approach using level lines, IEEE Trans. Image Processing, 11 (2002), 68-76.
    • (2002) IEEE Trans. Image Processing. , vol.11 , pp. 68-76
    • Masnou, S.1
  • 41
    • 53949088447 scopus 로고    scopus 로고
    • A non-local regularization strategy for image deconvolution
    • M. Mignotte, A non-local regularization strategy for image deconvolution, Pattern Recognition Letters, 29 (2008), 2206-2212.
    • (2008) Pattern Recognition Letters , vol.29 , pp. 2206-2212
    • Mignotte, M.1
  • 42
    • 17444406259 scopus 로고    scopus 로고
    • Smooth minimization of non-smooth functions
    • Y. Nesterov, Smooth minimization of non-smooth functions, Math. Program. Ser. A, 103 (2005), 127-152.
    • (2005) Math. Program. Ser. A. , vol.103 , pp. 127-152
    • Nesterov, Y.1
  • 43
    • 0029938380 scopus 로고    scopus 로고
    • Emergence of simple-cell receptive-eld properties by learning a sparse code for natural images
    • B. A. Olshausen and D. J. Field, Emergence of simple-cell receptive-eld properties by learning a sparse code for natural images, Nature, 381 (1996), 607-609.
    • (1996) Nature , vol.381 , pp. 607-609
    • Olshausen, B.A.1    Field, D.J.2
  • 44
    • 85032751363 scopus 로고    scopus 로고
    • Super-resolution image reconstruction: A technical overview
    • S. C. Park, M. K. Park and M. G. Kang, Super-resolution image reconstruction: A technical overview, IEEE Signal Processing Magazine, 20 (2003), 21-36.
    • (2003) IEEE Signal Processing Magazine , vol.20 , pp. 21-36
    • Park, S.C.1    Park, M.K.2    Kang, M.G.3
  • 45
    • 55149083501 scopus 로고    scopus 로고
    • Image processing with non-local spectral bases
    • G. Peyré, Image processing with non-local spectral bases, SIAM Multiscale Modeling and Simulation, 7 (2008), 703-730.
    • (2008) SIAM Multiscale Modeling and Simulation , vol.7 , pp. 703-730
    • Peyré, G.1
  • 46
    • 67349215512 scopus 로고    scopus 로고
    • Sparse modeling of textures
    • G. Peyré, Sparse modeling of textures, J. Math. Imaging Vis., 34 (2009), 17-31.
    • (2009) J. Math. Imaging Vis. , vol.34 , pp. 17-31
    • Peyré, G.1
  • 47
    • 56749176252 scopus 로고    scopus 로고
    • Non-local regularization of inverse problems
    • In "D. A. Forsyth, P. H. S. Torr and A. Zisserman, editors, ECCV'08,", Springer
    • G. Peyré, S. Bougleux and L. D. Cohen, Non-local regularization of inverse problems, In "D. A. Forsyth, P. H. S. Torr and A. Zisserman, editors, ECCV'08," volume 5304 of "Lecture Notes in Computer Science," pages 57-68. Springer, 2008.
    • (2008) Lecture Notes in Computer Science , vol.5304 , pp. 57-68
    • Peyré, G.1    Bougleux, S.2    Cohen, L.D.3
  • 49
    • 52349092455 scopus 로고    scopus 로고
    • On sparse reconstruction from fourier and gaussian measurements
    • M. Rudelson and R. Vershynin, On sparse reconstruction from fourier and gaussian measurements, Commun. on Pure and Appl. Math., 61 (2008), 1025-1045.
    • (2008) Commun. on Pure and Appl. Math. , vol.61 , pp. 1025-1045
    • Rudelson, M.1    Vershynin, R.2
  • 50
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), 259-268.
    • (1992) Phys. D. , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 51
    • 77952927821 scopus 로고
    • Computation of the fast walsh-fourier transform
    • J. Shanks, Computation of the fast walsh-fourier transform, IEEE Transactions on Computers, C-18 (1969), 457-459.
    • (1969) IEEE Transactions on Computers , vol.18 C , pp. 457-459
    • Shanks, J.1
  • 53
    • 34249101846 scopus 로고    scopus 로고
    • A short time beltrami kernel for smoothing images and manifolds
    • A. Spira, R. Kimmel and N. Sochen, A short time beltrami kernel for smoothing images and manifolds, IEEE Trans. Image Processing, 16 (2007), 1628-1636.
    • (2007) IEEE Trans. Image Processing. , vol.16 , pp. 1628-1636
    • Spira, A.1    Kimmel, R.2    Sochen, N.3
  • 55
    • 0032319446 scopus 로고    scopus 로고
    • Bilateral ltering for gray and color images
    • C. Tomasi and R. Manduchi, Bilateral ltering for gray and color images, In "Proc. of ICCV.'98," pages 839-846, 1998.
    • (1998) Proc. of ICCV.'98. , pp. 839-846
    • Tomasi, C.1    Manduchi, R.2
  • 56
    • 17144426986 scopus 로고    scopus 로고
    • Vector-valued image regularization with PDEs: Acommon framework for dierent applications
    • D. Tschumperlé and R. Deriche, Vector-valued image regularization with PDEs: Acommon framework for dierent applications, IEEE Trans. Pattern Anal. Mach. Intell, 27 (2005), 506-517.
    • (2005) IEEE Trans. Pattern Anal. Mach. Intell. , vol.27 , pp. 506-517
    • Tschumperlé, D.1    Deriche, R.2
  • 57
    • 0035533631 scopus 로고    scopus 로고
    • Convergence of a block coordinate descent method for nondierentiable minimization
    • P. Tseng, Convergence of a block coordinate descent method for nondierentiable minimization, Journal of Optimization Theory and Applications, 109 (2001), 475-494.
    • (2001) Journal of Optimization Theory and Applications , vol.109 , pp. 475-494
    • Tseng, P.1
  • 58
    • 0034448271 scopus 로고    scopus 로고
    • Fast texture synthesis using tree-structured vector quantization
    • ACM Press/Addison-Wesley Publishing Co
    • L-Y. Wei and M. Levoy, Fast texture synthesis using tree-structured vector quantization, In "Proc. of SIGGRAPH.'00," pages 479-488, ACM Press/Addison-Wesley Publishing Co., 2000.
    • (2000) Proc. of SIGGRAPH.'00. , pp. 479-488
    • Wei, L.-Y.1    Levoy, M.2
  • 60
    • 78149463074 scopus 로고    scopus 로고
    • Bregmanized nonlocal regularization for deconvolution and sparse reconstruction
    • X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, SIAM Journal on Imaging Sciences, 3 (2010), 253-276.
    • (2010) SIAM Journal on Imaging Sciences , vol.3 , pp. 253-276
    • Zhang, X.1    Burger, M.2    Bresson, X.3    Osher, S.4
  • 61
    • 27244449175 scopus 로고    scopus 로고
    • In "W. G. Kropatsch, R. Sablatnig and A. Hanbury, editors, German Pattern Recognition Symposium" Springer
    • D. Zhou and B. Scholkopf, Regularization on discrete spaces, In "W. G. Kropatsch, R. Sablatnig and A. Hanbury, editors, German Pattern Recognition Symposium," volume 3663, pages 361-368, Springer, 2005.
    • (2005) Regularization on discrete spaces , vol.3663 , pp. 361-368
    • Zhou, D.1    Scholkopf, B.2


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