Adaptive regularization of the NL-means: Application to image and video denoising

IEEE Transactions on Image Processing

Volumn 23, Issue 8, 2014, Pages 3506-3521

  Sutour, Camille ^a   Deledalle, Charles Alban ^a   Aujol, Jean François ^a  

^a UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

adaptive filtering; image and video denoising; Nonlocal means; total variation regularization

Indexed keywords

ADAPTIVE FILTERING; IMAGE PROCESSING; TEXTURES; VIDEO SIGNAL PROCESSING;

ADAPTIVE REGULARIZATION; ADAPTIVE TOTAL VARIATIONS; EXPONENTIAL FAMILY; NON-LOCAL MEANS; TOTAL VARIATION MINIMIZATION; TOTAL VARIATION REGULARIZATION; VARIATIONAL APPROACHES; VIDEO DE-NOISING;

IMAGE DENOISING;

ALGORITHM; ARTIFACT; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; PHOTOGRAPHY; PROCEDURES; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL NOISE RATIO; SIGNAL PROCESSING; STATISTICAL MODEL; VIDEORECORDING;

ALGORITHMS; ARTIFACTS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, STATISTICAL; PHOTOGRAPHY; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; SIGNAL-TO-NOISE RATIO; VIDEO RECORDING;

EID: 84904203906     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2014.2329448     Document Type: Article

References (60)

1. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, vol. 60, no. 1, pp. 259-268, 1992.
2. G. Gilboa, N. Sochen, and Y. Y. Zeevi, "Variational denoising of partly textured images by spatially varying constraints," IEEE Trans. Image Process., vol. 15, no. 8, pp. 2281-2289, Aug. 2006. (Pubitemid 44089102)
3. A. Buades, B. Coll, and J.-M. Morel, "A review of image denoising algorithms, with a new one," Multiscale Model. Simul., vol. 4, no. 2, pp. 490-530, Sep. 2005. (Pubitemid 43890582)
4. M. Mahmoudi and G. Sapiro, "Fast image and video denoising via non-local means of similar neighborhoods," IEEE Signal Process. Lett., vol. 12, no. 12, pp. 839-842, Dec. 2005. (Pubitemid 41800447)
5. C. Kervrann and J. Boulanger, "Optimal spatial adaptation for patchbased image denoising," IEEE Trans. Image Process., vol. 15, no. 10, pp. 2866-2878, Oct. 2006. (Pubitemid 44473632)
6. C. Kervrann and J. Boulanger, "Local adaptivity to variable smoothness for exemplar-based image regularization and representation," Int. J. Comput. Vis., vol. 79, no. 1, pp. 45-69, 2008.
7. M. V. de Ville and D. Kocher, "Non-local means with dimensionality reduction and SURE-based parameter selection," IEEE Trans. Image Process., vol. 20, no. 9, pp. 2683-2690, Sep. 2011.
8. H. Talebi, X. Xhu, and P. Milanfar, "How to SAIF-ly boost denoising performance," IEEE Trans. Image Process., vol. 22, no. 4, pp. 1470-1485, Apr. 2013.
9. C. Louchet and L. Moisan, "Total variation as a local filter," SIAM J. Imag. Sci., vol. 4, no. 2, pp. 651-694, 2011.
10. C.-A. Deledalle, V. Duval, and J. Salmon, "Non-local methods with shape-adaptive patches (NLM-SAP)," J. Math. Imag. Vis., vol. 43, no. 2, pp. 1-18, 2011.
11. S. Kindermann, S. Osher, and P. Jones, "Deblurring and denoising of images by nonlocal functionals," SIAM J. Multiscale Model. Simul., vol. 4, no. 4, pp. 1091-1115, 2005. (Pubitemid 44932284)
12. G. Gilboa and S. Osher, "Nonlocal operators with applications to image processing," Multiscale Model. Simul., vol. 7, no. 3, pp. 1005-1028, 2008.
13. G. Peyré, S. Bougleux, and L. D. Cohen, "Non-local regularization of inverse problems," Inverse Problems Imag., vol. 5, no. 2, pp. 511-530, 2011.
14. X. Zhang, M. Burger, X. Bresson, and S. Osher, "Bregmanized nonlocal regularization for deconvolution and sparse reconstruction," SIAM J. Imag. Sci., vol. 3, no. 3, pp. 253-276, 2010.
15. M. Protter, M. Elad, H. Takeda, and P. Milanfar, "Generalizing the non-local means to super-resolution reconstruction," IEEE Trans. Image Process., vol. 18, no. 1, pp. 36-51, Jan. 2009.
16. E. d'Angelo and P. Vandergheynst, "Fully non-local super-resolution via spectral hashing," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., ICASSP, May 2011, pp. 1137-1140.
17. M. Mignotte, "A non-local regularization strategy for image deconvolution," Pattern Recognit. Lett., vol. 29, no. 16, pp. 2206-2212, 2008.
18. A. Buades, B. Coll, and J.-M. Morel, "Denoising image sequences does not require motion compensation," in Proc. IEEE Conf. Adv. Vid. Signal Based Surveill., AVSS, Sep. 2005, pp. 70-74.
19. Y. Wexler, E. Shechtman, and M. Irani, "Space-time completion of video," IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 3, pp. 463-476, Mar. 2007. (Pubitemid 46336421)
20. A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imag. Vis., vol. 20, pp. 89-97, Aug. 2004.
21. P. Combettes and J. Pesquet, Proximal Splitting Methods in Signal Processing. New York, NY, USA: Springer-Verlag, Jan. 2010.
22. A. Chambolle and T. Pock, "A first-order primal-dual algorithm for convex problems with applications to imaging," J. Math. Imag. Vis., vol. 40, no. 1, pp. 120-145, 2011.
23. P. C. Hansen and D. P. O'Leary, "The use of the l-curve in the regularization of discrete ill-posed problems," SIAM J. Sci. Comput., vol. 14, no. 6, pp. 1487-1503, 1993.
24. S. Ramani, T. Blu, and M. Unser, "Monte-carlo sure: A black-box optimization of regularization parameters for general denoising algorithms," IEEE Trans. Image Process., vol. 17, no. 9, pp. 1540-1554, Sep. 2008.
25. J. Polzehl and V. Spokoiny, "Propagation-separation approach for local likelihood estimation," Probab. Theory Rel. Fields, vol. 135, no. 3, pp. 335-362, Jul. 2006. (Pubitemid 43593358)
26. C.-A. Deledalle, L. Denis, and F. Tupin, "Iterative weighted maximum likelihood denoising with probabilistic patch-based weights," IEEE Trans. Image Process., vol. 18, no. 12, pp. 2661-2672, Dec. 2009.
27. C.-A. Deledalle, L. Denis, and F. Tupin, "How to compare noisy patches? Patch similarity beyond gaussian noise," Int. J. Comput. Vis., vol. 99, no. 1, pp. 86-102, 2012.
28. C. Kervrann, J. Boulanger, and P. Coupé, "Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal," in Scale Space and Variational Methods in Computer Vision. New York, NY, USA: Springer-Verlag, 2007, pp. 520-532. (Pubitemid 350269823)
29. P. Coupé, P. Hellier, C. Kervrann, and C. Barillot, "Bayesian non local means-based speckle filtering," in Proc. 5th IEEE Int. Symp. Biomed. Imag. ISBI, May 2008, pp. 1291-1294.
30. H. Zhong, Y. Li, and L. Jiao, "SAR image despeckling using bayesian nonlocal means filter with sigma preselection," IEEE Geosci. Remote Sens. Lett., vol. 8, no. 4, pp. 809-813, Apr. 2011.
31. C.-A. Deledalle, L. Denis, F. Tupin, A. Reigber, and M. Jager, "NLSAR: A unified non-local framework for resolution-preserving (pol)(in) SAR denoising," IEEE Trans. Geosci. Remote Sens., (under minor revision).
32. V. Duval, J.-F. Aujol, and Y. Gousseau, "A biais-variance approach for the non-local means," SIAM J. Imag. Sci., vol. 4, no. 2, pp. 760-788, 2011.
33. J.-S. Lee, "Refined filtering of image noise using local statistics," Comput. Graph. Image Process., vol. 15, no. 4, pp. 380-389, 1981.
34. D. T. Kuan, A. A. Sawchuk, T. C. Strand, and P. Chavel, "Adaptive noise smoothing filter for images with signal-dependent noise," IEEE Trans. Pattern Anal. Mach. Intell., vol. 7, no. 2, pp. 165-177, Mar. 1985. (Pubitemid 15463696)
35. A. Chambolle and P. Lions, "Image recovery via total variation minmization and related problems," Numer. Math., vol. 76, no. 2, pp. 167-188, Apr. 1997.
36. D. L. Donoho and J. M. Johnstone, "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, 1994.
37. S. P. Awate and R. T. Whitaker, "Unsupervised, information- theoretic, adaptive image filtering for image restoration," IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 3, pp. 364-376, Mar. 2006. (Pubitemid 43159633)
38. T. Brox and D. Cremers, "Iterated nonlocal means for texture restoration," in Scale Space and Variational Methods in Computer Vision, Berlin, Germany: Springer-Verlag, 2007, pp. 13-24. (Pubitemid 350269781)
39. A. Buades, B. Coll, and J.-M. Morel, "Image enhancement by non-local reverse heat equation," CMLA-ENS-Cachan, Cachan, France, Tech. Rep. 22, Mar. 2006.
40. P. Arias, V. Caselles, and G. Facciolo, "Analysis of a variational framework for exemplar-based image inpainting," Multiscale Model. Simul., vol. 10, no. 2, pp. 473-514, 2012.
41. D. Zhou and B. Scholkopf, "A regularization framework for learning from graph data," in Proc. Workshop Statist. Rel. Learn. Connections Fields, 2004.
42. S. Bougleux, A. Elmoataz, and M. Melkemi, "Discrete regularization on weighted graphs for image and mesh filtering," in Scale Space and Variational Methods in Computer Vision. New York, NY, USA: Springer- Verlag, 2007, pp. 128-139. (Pubitemid 350269790)
43. G. Gilboa and S. Osher, "Nonlocal linear image regularization and supervised segmentation," SIAM Multiscale Model. Simul., vol. 6, no. 2, pp. 595-630, 2007.
44. M. Collins, S. Dasgupta, and R. E. Schapire, "A generalization of principal components analysis to the exponential family," in Proc. Neural Inform. Process. Syst., NIPS, 2002, pp. 617-624.
45. J. Darbon, A. Cunha, T. Chan, S. Osher, and G. Jensen, "Fast non-local filtering applied to electron cryomicroscopy," in Proc. IEEE Int. Symp. Biomed. Imag., ISBI, May 2008, pp. 1331-1334.
46. S. Anthoine, J.-F. Aujol, Y. Boursier, and C. Mélot, "Some proximal methods for poisson intensity CBCT and PET," Inverse Problems Imag., vol. 6, no. 4, pp. 565-598, 2012.
47. G. Aubert and J.-F. Aujol, "A variational approcah to removing multiplicative noise," SIAM J. Appl. Math., vol. 68, no. 4, pp. 925-946, 2008.
48. P. Combettes and V. Wajs, "Signal recovery by proximal forwardbackward splitting," Multiscale Model. Simul., vol. 4, no. 4, pp. 1168-1200, 2005. (Pubitemid 44932287)
49. A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imag. Sci., vol. 2, no. 1, pp. 183-202, 2009.
50. H. Raguet, J. Fadili, and G. Peyré, "Generalized forward-backward splitting," SIAM J. Imag. Sci., vol. 6, no. 3, pp. 1199-1226, 2013.
51. A. Beck and M. Teboulle, "Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems," IEEE Trans. Image Process., vol. 18, no. 11, pp. 2419-2434, Nov. 2009.
52. A. Buades, B. Coll, and J.-M. Morel, "Nonlocal image and movie denoising," Int. J. Comput. Vis., vol. 76, no. 2, pp. 123-139, 2008.
53. C. Liu and W. Freeman, "A high-quality video denoising algorithm based on reliable motion estimation," in Proc. Eur. Conf. Comput. Vis., ECCV, 2010, pp. 706-719.
54. Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, "Image quality assessment: From error visibility to structural similarity," IEEE Trans. Image Process., vol. 13, no. 4, pp. 600-612, Apr. 2004.
55. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Image denoising by sparse 3-D transform-domain collaborative filtering," IEEE Trans. Image Process., vol. 16, no. 8, pp. 2080-2095, Aug. 2007. (Pubitemid 47225460)
56. M. Mäkitalo and A. Foi, "Poisson-Gaussian denoising using the exact unbiased inverse of the generalized anscombe transformation," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., ICASSP, Mar. 2012, pp. 1081-1084.
57. H. Xie, L. Pierce, and F. Ulaby, "Statistical properties of logarithmically transformed speckle," IEEE Trans. Geosci. Remote Sens., vol. 40, no. 3, pp. 721-727, Mar. 2002. (Pubitemid 34692250)
58. M. Makitalo, A. Foi, D. Fevralev, and V. Lukin, "Denoising of singlelook SAR images based on variance stabilization and nonlocal filters," in Proc. Int. Conf. Math. Methods Electromagn, Theory, MMET, 2010, pp. 1-4.
59. K. Dabov, A. Foi, and K. Egiazarian, "Video denoising by sparse 3D transform-domain collaborative filtering," in Proc. 15th Eur. Signal Process. Conf., Poznan, Poland, 2007.
60. M. Maggioni, G. Boracchi, A. Foi, and K. Egiazarian, "Video denoising, deblocking and enhancement through separable 4-D nonlocal spatiotemporal transforms," IEEE Trans. Image Process., vol. 21, no. 9, pp. 3952-3966, Oct. 2012.