Image deblurring in the presence of impulsive noise

International Journal of Computer Vision

Volumn 70, Issue 3, 2006, Pages 279-298

  Bar, Leah ^a   Kiryati, Nahum ^a   Sochen, Nir ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Image deblurring; Impulse noise; Restoration; Salt and pepper noise; Variational methods

Indexed keywords

IMAGE RECONSTRUCTION; IMPULSE NOISE; MATHEMATICAL MODELS; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); STATISTICAL METHODS;

ANISOTROPIC DIFFUSION; IMAGE DEBLURRING; SALT AND PEPPER NOISE; VARIATIONAL METHODS;

IMAGE PROCESSING;

EID: 33746391916     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-006-6468-1     Document Type: Conference Paper

References (48)

1. Acar, R. and Vogel, C.R., 1994. "Analysis of Total Variation Penalty Methods", Inverse Problems, Vol. 10, pp. 1217-1229.
2. 1-Norm of the Gradient and their Approximation", Interfaces and Five Boundaries, Vol. l, pp. 17-37.
3. Ambrosio, L. and Tortorelli, V.M., 1990. "Approximation of Functionals Depending on Jumps by Elliptic Functionals via Γ- Convergence", Communications on Pute and Applied Mathematics, Vol. XLIII, pp. 999-1036.
4. Arce, G.R., Paredes, J.L. and Mullan, J., 2000. "Nonlinear Filtering for Image Analysis and Enhancement", in Bovik, A.L. (Ed.), Handbook of Image & Video Processing, Academic Press.
5. Aubert, G. and Kornprobst, P., 2002. Mathematical Problems in Image Processing, Springer, New York.
6. Aubert, G., Blanc-Féraud, L. and March, R., 2004. "Γ-Convergence of Discrete Functionals with Nonconvex Perturbation for Image Classification", SIAM Journal of Numerical Analysis, Vol. 42, pp. 1128-1145.
7. Banham, M. and Katsaggelos, A., 1997. "Digital Image Restoration", IEEE Signal Processing Mag., Vol. 14, pp. 24-41.
8. Bar, L., Sochen, N. and Kiryati, N., 2004. "Variational Pairing of Image Segmentation and Blind Restoration", Proc. ECCV'2004, Prague, Czech Republic, Part II: LNCS #3022, pp. 166-177, Springer.
9. Bar, L., Sochen, N. and Kiryati, N., 2005. "Image Deblurring in the Presence of Salt and Pepper Noise", Proc. Scale-Space 2005, Hofgeismar, Germany: LNCS #3459, pp. 107-118, Springer.
10. 1 -Unified Variational Framework for Image Restoration", Proc. ECCV'2004, Prague, Czech Republic, Part IV: LNCS #3024, pp. 1-13, Springer.
11. Black, M.J. and Rangarajan, A., 1996. "On the Unification of Line Processes, Outlier Rejection, and Robust Statistics with Applications in Early Vision", International Journal of Computer Vision, Vol. 19, pp. 57-92.
12. Black, M.J., Sapiro, G., Marimont, D., and Heeger, D., 1998. "Robust Anisotropic Diffusion", IEEE Trans. Image Processing, Vol. 7, pp. 421-432.
13. Braides, A., 1998. Approximation of Free-Discontinuity Problems, Lecture Notes in Mathematics, Vol. 1694, Springer-Verlag.
14. Brook, A., Kimmel, R. and Sochen, N., 2003. "Variational Segmentation for Color Images", International Journal of Computer Vision, Vol. 18, pp. 247-268.
15. Brox, T., Brunn, A., Papenberg, N. and Weickert, J., 2004. "High Accuracy Optical Flow Estimation Based on a Theory for Warping", Proc. ECCV'2004, Prague, Czech Republic, Part IV: LNCS #3024, pp. 25-36, Springer.
16. Catté, F., Lions, PL., Morel, J.M., and Coll, T., 1992. "Image Selective Smoothing and Edge Detection by Nonlinear Diffusion", SIAM Journal of Numerical Analysis, Vol. 29,pp. 182-193.
17. Chan, R.H., Ho, C. and Nikolova, M., 2005. "Salt-and-Pepper Noise Removal by Median-type Noise Detectors and Detailpreserving Regularization" , IEEE Transactions on Image Processing, 14:1479-1485.
18. Chan, T.F. and Wong, C., 1998. "Total Variation Blind Deconvolution", IEEE Trans. Image Processing, Vol. 7, pp. 370-375
19. Charbonnier, P., Blanc-Féraud, L., Aubert, G., and Barlaud, M., 1997. "Deterministic Edge-Preserving Regularization in Computed Imaging", IEEE Trans. Image Processing, Vol. 6, pp. 298-311.
20. Chen, T. and Wu, H.R., 2001. "Space Variant Median Filters for the Restoration of Impulse Noise Corrupted Images", IEEE Trans. Circuits and Systems II, Vol. 48, pp. 784-789.
21. Chipot, M., March, R., Rosati, M., and Vergara Caffarelli, G., 1997. "Analysis of a Nonconvex Problem Related to Signal Selective Smoothing", Mathematical Models and Methods in Applied Science, Vol. 7, pp. 313-328.
22. Dal Maso, G., 1993. An Introduction to Γ-Convergence, Progress in Nonlinear Differential Equations and their Applications, Birkhauser.
23. Durand, S. and Froment, J., 2003. "Reconstruction of Wavelet Coefficients Using Total Variation Minimization", SIAM Journal of Scientific Computing, Vol. 24, pp. 1754-1767.
24. Durand, S. and Nikolova, M., 2003. "Restoration of Wavelet Coefficients by Minimizing a Specially Designed Objective Function", Proc. IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, pp. 145-152.
25. Geman, D. and Reynolds, G., 1992. "Constrained Restoration and the Recovery of Discontinuities", IEEE Tram. Pattern Analysis and Machine Intelligence, Vol. 14, pp. 367-383.
26. Geman, S. and Geman, D., 1984. "Stochastic Relaxation, Gibbs Distributions and Bayesian Restoration of Images", IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 6, pp. 721-741.
27. Geman, S. and McClure, D.E., 1987. "Statistical Methods for Tomographic Image Reconstruction", Bulletin of the International Statistical Institute, LII-4, pp. 5-21.
28. Huber, P.J., 1981. Robust Statistics, John Wiley and Sons, New York.
29. Hwang, H. and Haddad, R.A., 1995. "Adaptive Median Filters: New Algorithms and Results", IEEE Trans. Image Processing, Vol. 4, pp. 499-502.
30. Malgouyres, F., 2002. "Minimizing the Total Variation Under a General Convex Constraint", IEEE Trans. Image Processing, Vol. 11, pp. 1450-1456.
31. Mumford, D. and Shah, J., 1989. "Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems", Communications on Pure and Applied Mathematics, Vol. 42, pp. 577-684.
32. Nikolova, M., 2002. "Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms: Application to the Processing of Outliers", SIAM Journal on Numerical Analysis, Vol. 40, pp. 965-994.
33. Nikolova, M., 2004. "A Variational Approach to Remove Outliers and Impulse Noise", Journal of Mathematical Imaging and Vision, Vol. 20, pp. 99-120.
34. Nordstrom, N., 1990. "Biased Anisotropic Diffusion - A Unified Regularization and Diffusion Approach to Edge Detection", Proc. 1st European Conference on Computer Vision, pp. 18-27, Antibes, France.
35. Perona, P. and Malik, J., 1990. "Scale Space and Edge Detection Using Anisotropie Diffusion", IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 12, pp. 629-639.
36. Pok, G., Liu, J.-C. and Nair, A.S., 2003. "Selective Removal of Impulse Noise based on Homogeneity Level Information", IEEE Trans. Image Processing, Vol. 12, pp. 85-92.
37. Rondi, L. and Santosa, F., 2001. "Enhanced Electrical Impedance Tomography via the Mumford-shah Functional", ESAIM: Control, Optimization and Calculus of Variations, Vol. 6, pp. 517-538.
38. Rosati, M., 2000. "Asymptotic Behavior of a Geman and McClure Discrete Model", Applied Math. Optim., Vol. 41, pp. 51-85.
39. Rudin, L. and Osher, S., 1994. "Total Variation Based Image Restoration with Free Local Constraints", Proc. IEEE ICIP, Vol. 1, pp. 31-35, Austin TX, USA.
40. Rudin, L., Osher, S. and Fatemi, E., 1992. "Non Linear Total Variation Based Noise Removal Algorithms", Physica D, Vol. 60, pp. 259-268.
41. Shah, J., 1996. "A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion", Proc. IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, pp. 136-142.
42. Sochen, N., Kimmel, R. and Malladi, R., 1998. "A General Framework for Low level Vision" IEEE Trans. Image Processing, Vol. 7, pp. 310-318.
43. Teboul, S., Blanc-Féraud, L., Aubert, G., and Barlaud, M., 1998. "Variational Approach for Edge-Preserving Regularization Using Coupled PDE's", IEEE Trans. Image Processing, Vol. 7, pp. 387-397.
44. Tikhonov, A. and Arsenin, V., 1997. Solutions of Ill-posed Problems, New York.
45. Vogel, C. and Oman, M., 1998. "Fast, Robust Total Variation-based Reconstruction of Noisy, Blurred Images", IEEE Trans. Image Processing, Vol. 7, pp. 813-824.
46. Weickert, J., 1994. "Anisotropic Diffusion Filters for Image Processing Based Quality Control", Proc. Seventh European Conference on Mathematics in Industry, Teubner, Stuttgart, pp. 355-362.
47. Weickert, J., 1999. "Coherence-Enhancing Diffusion Filtering", International Journal of Computer Vision, Vol. 31, pp. 111-127.
48. Weisstein, E.W. et al, "Minimal Residual Method", from MathWorld-A Wolfram Web Resource. http://mathworld.wolfram. com/ MinimalResidualMethod.html.