Deblurring of color images corrupted by impulsive noise

IEEE Transactions on Image Processing

Volumn 16, Issue 4, 2007, Pages 1101-1111

  Bar, Leah ^a   Brook, Alexander ^b   Sochen, Nir ^c   Kiryati, Nahum ^c  

^a University of Minnesota   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

Color image processing; Deblurring; Denoising; Impulse noise; Mumford Shah (MS) functional

Indexed keywords

APPROXIMATION THEORY; EDGE DETECTION; IMAGE QUALITY; IMAGE RECONSTRUCTION; IMPULSE NOISE;

DEBLURRING; DENOISING; MUMFORD-SHAH FUNCTIONAL;

COLOR IMAGE PROCESSING;

ALGORITHM; ARTICLE; ARTIFACT; ARTIFICIAL INTELLIGENCE; COLOR; COLORIMETRY; COMPUTER ASSISTED DIAGNOSIS; EVALUATION; IMAGE ENHANCEMENT; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY;

ALGORITHMS; ARTIFACTS; ARTIFICIAL INTELLIGENCE; COLOR; COLORIMETRY; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 34047214120     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2007.891805     Document Type: Article

References (53)

1. G. Demoment, "Image reconstruction and restoration: Overview of common estimation structures and problems," IEEE Trans. Acoust. Speech, Signal Process., vol. 37, no. 12, pp. 2024-2036, Dec, 1989.
2. J. Biemond, R. Lagendijk, and R. Mersereau, "Iterative methods for image deblurring," Proc. IEEE, vol. 78, no. 5, pp. 856-883, May 1990.
3. M. Banham and A. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag., vol. 14, no. 2, pp. 24-41, Mar. 1997.
4. R. Puetter, T. Gosnell, and A. Yahil, "Digital image reconstruction: Deblurring and denoising," Annu. Rev. Astron. Astrophys., vol. 43, pp. 139-194, 2005.
5. L. Rudin, S. Osher, and E. Fatemi, "Non linear total variatrion based noise removal algorithms," Phys. D, vol. 60, pp. 259-268, 1992.
6. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-6, no. 6, pp. 721-741, Nov. 1984.
7. C. Vogel and M. Oman, "Iterative methods for total variation denoising," SIAM J. Sci. Comput., vol. 17, no. 1, pp. 227-238, Jan. 1996.
8. C. Vogel and M. Oman,, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process., vol. 7, no. 6, pp. 813-824, Jun. 1998.
9. D. Geman and G. Reynolds, "Constrained restoration and recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 3, pp. 367-383, Mar. 1992.
10. D. Geman and C. Yang, "Nonlinear image recovery with half-quadratic regularization," IEEE Trans. Image Process., vol. 4, no. 7, pp. 932-946, Jul. 1995.
11. R. Neelmani, H. Choi, and R. Baraniuk, "Forward: Fourier-wavelet regularized deconvolution for ill-conditioned systems," IEEE Trans. Image Process., vol. 52, no. 2, pp. 418-433, Feb. 2004.
12. M. Nikolova, J. Idier, and A. Mohammad-Djafari, "Inversion of large-support ill-posed linear operators using a piecewise gaussian MRF," IEEE Trans. Image Process., vol. 8, no. 4, pp. 571-578, Apr. 1998.
13. P. Combettes and J. Luo, "An adaptive level set method for nondifferentiable constrained image recovery," IEEE Trans. Image Process., vol. 11, no. 11, pp. 1295-1304, Nov. 2002.
14. M. Nikolova, "Minimizers of cost-functions involving nonsmooth data-fidelity y terms: Application to the processing of outliers," SIAM J. Numer. Anal., vol. 40, pp. 965-994, 2002.
15. M. Nikolova, "A variational approach to remove outliers and impulse noise," J. Math. Imag. Vis., vol. 20, pp. 99-120, 2004.
16. R. Chan, C. Ho, and M. Nikolova, "Salt-and-pepper noise removal by median-type noise detectors and edge-preserving regularization," IEEE Trans. Image Process., vol. 14, no. 10, pp. 1479-1485, Oct. 2005.
17. N. Galatsanos, M. Wernick, A. Katsaggelos, and R. Molina, "Multichannel image recovery," in Handbook of Image and Video Processing, A. C. Bovik, Ed., 2nd ed. New York: Academic, 2005, pp. 203-218.
18. A. Brook, R. Kimmel, and N. Sochen, "Variational restoration and edge detection for color images," J. Math. Imag. Vis., vol. 18, pp. 247-268, 2003.
19. D. Tschumperlé, "PDEs based regularization of multivalued images and applications," Ph.D. dissertation, Univ. Nice-Sophia Antipolis, Sophia Antipolis, France, 2002.
20. S. Di Zenzo, "A note on the gradient of a multi-image," Comput. Vis., Graph., Image Process., vol. 33, no. 1, pp. 116-125, 1986.
21. A. Cumani, "Edge detection in multispectral images," CVGIP: Graph. Models Image Process., vol. 53, no. 1, pp. 40-51, 1991.
22. G. Sapiro and D. Ringach, "Anisotropic diffusion of multivalued images with application to color filtering," IEEE Trans. Image Process., vol. 5, no. 10, pp. 1582-1586, Oct. 1996.
23. P. Blomgren, "Total variation methods for restoration of vector valued images," Ph.D. dissertation, Univ. California, Los Angeles, CA, 1998.
24. N. Sochen, R. Kimmel, and R. Malladi, "A general framework for low level vision," IEEE Trans. Image Process., vol. 7, no. 3, pp. 310-318, Mar. 1998.
25. D. Barash, "One-step deblurring and denoising color images using partial differential equations," presented at the 1st SIAM Conf. Imaging Science, Boston, MA, 2002.
26. M. Welk, D. Theis, T. Brox, and J. Weickert, "PDE-based deconvolution with forward-backward diffusivities and diffusion tensors," in Proc. 5th Int. Conf. Scale Space and PDE Methods in Computer Vision, 2005, vol. 3439, pp. 585-597.
27. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 7, pp. 629-639, Jul. 1990.
28. R. Molina, J. Mateos, A. Katsaggelos, and M. Vega, "Bayesian multichannel image restoration using compound Gauss-Markov random fields," IEEE Trans. Image Process., vol. 12, no. 12, pp. 1642-1654, Dec. 2003.
29. J. Astola, P. Haavisto, and Y. Neuvo, "Vector median filters," Proc. IEEE, vol. 78, no. 4, pp. 678-689, Apr. 1990.
30. P. Trahanias and A. Venetsanopoulos, "Vector directional filters - A newclass of multichannel image processing filters," IEEE Trans. Image Process., vol. 2, no. 4, pp. 528-534, Oct. 1993.
31. P. Trahanias, D. Karakos, and A. Venetsanopoulos, "Directional processing of color images: Theory and experimental results," IEEE Trans. Image Process., vol. 5, no. 6, pp. 868-880, Jun. 1996.
32. H. Hwang and R. Haddad, "Adaptive median filters: New algorithms and results," IEEE Trans. Image Process., vol. 4, no. 4, pp. 499-502, Apr. 1995.
33. F. Cheikh, R. Hamila, M. Gabbouj, and J. Astola, "Impulse noise removal in highly corrupted color images," in Proc. Int. Conf. Image Processing, 1996, vol. 1, pp. 997-1000.
34. R. Lukac, B. Smolka, K. Martin, K. Plataniotis, and A. Venetsanopoulos, "Vector filtering for color imaging," IEEE Signal Process. Mag., vol. 22, no. 1, pp. 74-86, Jan. 2005.
35. L. Bar, N. Sochen, and N. Kiryati, "Image deblurring in the presence of salt-and-pepper noise," in Proc. 5th Int. Conf. Scale Space and PDE Methods in Computer Vision, 2005, vol. 3459, pp. 107-118.
36. L. Bar, N. Sochen, and N. Kiryati, "Image deblurring in the presence of impulsive noise," Int. J. Comput. Vis., vol. 70, pp. 279-298, 2006.
37. P. Huber, Robust Statistics. New York: Wiley, 1981.
38. M. Black and A. Rangarajan, "On the unification of line processes, outlier rejection, and robust statistics with applications in early vision," Int. J. Comput. Vis., vol. 19, pp. 57-92, 1996.
39. P. Blomgren and T. Chan, "Color TV: Total variation methods for restoration of vector-valued images," IEEE Trans. Image Process., vol. 7, no. 3, pp. 304-309, Mar. 1998.
40. R. Kimmel, R. Malladi, and N. Sochen, "Images as embedded maps and minimal surfaces: Movies, color, texture, and volumetric medical images," Int. J. Comput. Vis., vol. 39, pp. 111-129, 2000.
41. D. Mumford and J. Shah, "Optimal approximations by piecewise smooth functions and associated variational problems," Comm. Pure Appl. Math., vol. 42, pp. 577-685, 1989.
42. L. Bar, N. Sochen, and N. Kiryati, "Variational pairing of image segmentation and blind restoration," in Proc. 8th Eur. Conf. Computer Vision, 2004, vol. 3022, pp. 166-177.
43. L. Ambrosio and V. Tortorelli, "Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence," Comm. Pure Appl. Math., vol. 43, no. 8, pp. 999-1036, 1990.
44. J. Shah, "A common framework for curve evolution, segmentation and anisotropic diffusion," in Proc. IEEE Conf. Computer Vision and Pattern Recognition, 1996, pp. 136-142.
45. 1-norm of the gradient and their approximation," Interfaces Free Bound., vol. 1, pp. 17-37, 1999.
46. D. Strong and T. Chan, "Edge-preserving and scale dependent properties of total variation regularization," CAM Rep. 00-38, Math Dept., Univ. California, Los Angeles, 2000.
47. R. Kaftori, N. Sochen, and Y. Zeevi, "Color image denoising and blind deconvolution using the Beltrami operator," in Proc. 3rd Int. Symp. Image Signal Processing and Analysis, 2003, vol. 1, pp. 1-4.
48. L. Bar, "Variational image restoration with segmentation-based regularization," Ph.D. dissertation, Univ. Tel-Aviv, Tel-Aviv, Israel, 2006.
49. P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, "Deterministic edge-preserving regularization in computed imaging," IEEE Trans. Image Process., vol. 6, no. 2, pp. 298-311, Feb. 1997.
50. S. Geman and D. McClure, "Bayesian image analysis: An application to single photon emission tomography," Proc. Amer. Statist. Assoc. Statist. Comput. Section, pp. 12-18, 1985.
51. S. Teboul, L. Blanc-Féraud, G. Aubert, and M. Barlaud, "Variational approach for edge-preserving regularization using coupled PDE's," IEEE Trans. Image Process., vol. 7, no. 3, pp. 387-397, Mar. 1998.
52. M. Chipot, R. March, M. Rosati, and G. Caffarell, "Analysis of a non-convex problem related to signal selective smoothing," Math. Models Methods Appl. Sci., vol. 7, pp. 313-328, 1997.
53. C. Boncelet, "Image noise models," in Handbook of Image and Video Processing, A. C. Bovik, Ed. New York: Academic, 2000, pp. 325-335.