A Variational Approach to Remove Outliers and Impulse Noise

Journal of Mathematical Imaging and Vision

Volumn 20, Issue 1-2, 2004, Pages 99-120

  Nikolova, Mila ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Image denoising; Impulse noise removal; Non smooth analysis; Non smooth optimization; Outliers; Regularization; Restoration; Signal denoising; Total variation; Variational methods

Indexed keywords

DATA REDUCTION; FUNCTION EVALUATION; IMPULSE NOISE; OPTIMIZATION; SIGNAL DETECTION; SIGNAL FILTERING AND PREDICTION; STATISTICAL METHODS; VARIATIONAL TECHNIQUES;

IMAGE DENOISING; NON-SMOOTH OPTIMIZATION; OUTLIERS; REGULARIZATION; SIGNAL DENOISING; TOTAL VARIATION METHOD;

IMAGE ANALYSIS;

EID: 1242284980     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JMIV.0000011920.58935.9c     Document Type: Conference Paper

References (35)

1. E. Abreu, M. Lightstone, S.K. Mitra, and K. Arakawa, "A new efficient approach for the removal of impulse noise from highly corrupted images," IEEE Transactions on Image Processing, Vol. 5, pp. 1012-1025, 1996.
2. S. Alliney, "Digital filters as absolute norm regularizers," IEEE Transactions on Medical Imaging, Vol. MI-12, pp. 173-181, 1993.
3. S. Alliney, "A property of the minimum vectors of a regularizing functional defined by means of absolute norm," IEEE Transactions on Signal Processing, Vol. 45, pp. 913-917, 1997.
4. G.R. Arce, T.A. Hall, and K.E. Barner, "Permutation weighted order statistic filters," IEEE Transactions on Image Processing, Vol. 4, pp. 1070-1083, 1995.
5. J.E. Besag, "Digital image processing: Towards Bayesian image analysis," Journal of Applied Statistics, Vol. 16, pp. 395-407, 1989.
6. M. Black and A. Rangarajan, "On the unification of line processes, outlier rejection, and robust statistics with applications to early vision," International Journal of Computer Vision, Vol. 19, pp. 57-91, 1996.
7. C. Bouman and K. Sauer, "A generalized Gaussian image model for edge-preserving map estimation," IEEE Transactions on Image Processing, Vol. 2, pp. 296-310, 1993.
8. C. Bouman and K. Sauer, "A unified approach to statistical tomography using coordinate descent optimization," IEEE Transactions on Image Processing, Vol. 5, pp. 480-492, 1996.
9. A.C. Bovik, Handbook of Image and Video Processing, Academic Press: New York, 2000.
10. P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, "Deterministic edge-preserving regularization in computed imaging," IEEE Transactions on Image Processing, Vol. 6, pp. 298-311, 1997.
11. T. Chen and H.R. Wu, "Adaptive impulse detection using center-weighted median filters," IEEE Transactions on Image Processing, Vol. 8, pp. 1-3, 2001.
12. G. Demoment, "Image reconstruction and restoration: Overview of common estimation structure and problems," IEEE Transactions on Acoustics Speech and Signal Processing, Vol. ASSP-37, pp. 2024-2036, 1989.
13. M. Fisher and J. Paredes, "Weighted median image sharpeners for world wide web," IEEE Transactions on Image Processing, Vol. 11, pp. 717-727, 2002.
14. A. Flaig, G. R. Arce, and K. Barner, "Affine order statistics filters: Medianization of linear FIR filters," IEEE Transactions on Signal Processing, 1998.
15. D. Geman, "Random fields and inverse problems in imaging," Vol. 1427, École d'Été de Probabilités de Saint-Flour XVIII -1988, Springer-Verlag, Lecture Notes in Mathematics ed., 1990, pp. 117-193.
16. D. Geman and C. Yang, "Nonlinear image recovery with half-quadratic regularization," IEEE Transactions on Image Processing, Vol. IP-4, pp. 932-946, 1995.
17. R. Glowinski, J. Lions, and R. Trémolières, Analyse numérique des inéquations variationnelles, Vol. 1, 1st edition Dunod: Paris, 1976.
18. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Vols. I and II. Springer-Verlag: Berlin, 1996.
19. D. Keren and M. Werman, "Probabilistic analysis of regularization," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-15, pp. 982-995, 1993.
20. S.J. Ko and Y.H. Lee, "Center weighted median filters and their applications to image enhancement," IEEE Transactions on Circuits and Systems, Vol. 38, pp. 984-993, 1991.
21. Y.-H. Lee and S. Tantaratana, "Decision-based order statistic filters," IEEE Transactions on Acoustics Speech and Signal Processing, Vol. 38, pp. 406-420, 1990.
22. S. Li, "Markov random field modeling in computer vision," 1st edition. Springer-Verlag: New York, 1995.
23. M. Nikolova, "Markovian reconstruction using a GNC approach," IEEE Transactions on Image Processing, Vol. 8, pp. 1204-1220, 1999.
24. M. Nikolova, "Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers," SIAM Journal of Numerical Analysis, Vol. 40, pp. 965-994, 2001.
25. G. Pok and A.S. Nair, "Selective removal of impulse noise based on homogeneity level information," IEEE Transactions on Image Processing, Vol. 12, pp. 85-92, 2003.
26. L. Rudin, S. Osher, and C. Fatemi, "Nonlinear total variation based noise removal algorithm," Physica, Vol. 60 D, pp. 259-268, 1992.
27. J.-L. Starck, E.P., and F. Murtagh, "Deconvolution in astronomy: A review," Publications of the Astronomical Society of the Pacific, 114 2002.
28. A. Tarantola, Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier Science Publishers: Amsterdam, 1987.
29. A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems, Winston: Washington DC, 1977.
30. J.W. Tukey, "Nonlinear (nonsuperimposable) methods for smoothing data," in Conf. Rec., Eacson, 1974.
31. C.R. Vogel and M.E. Oman, "Iterative method for total variation denoising," SIAM Journal of Scientific Computing, Vol. 17, pp. 227-238, 1996.
32. C.R. Vogel and M.E. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Transactions on Image Processing, Vol. 7, pp. 813-824, 1998.
33. Z. Wang and D. Zhang, "Restoration of impulse noise corrupted images using long-range correlation," IEEE Signal Processing Letters, Vol. 5, pp. 4-7, 1998.
34. Windyga, "Fast impulsive noise removal," IEEE Transactions on Image Processing, Vol. 10, pp. 173-179, 2001.
35. L. Yin, R. Yang, M. Gabbouj, and Y. Neuvo, "Weighted median filters: A tutorial," IEEE Transactions on Circuit Theory, Vol. 41, pp. 157-192, 1996.