A total variation wavelet inpainting model with multilevel fitting parameters

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 6313, Issue , 2006, Pages

  Chan, Tony F ^a   Shen, Jianhong ^b   Zhou, Hao Min ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of Minnesota   (United States)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NOISY IMAGES; WAVELET COEFFICIENTS; WAVELET INPAINTING MODELS;

CURVE FITTING; MATHEMATICAL MODELS; NATURAL FREQUENCIES; NUMERICAL ANALYSIS; WAVELET TRANSFORMS;

IMAGE COMMUNICATION SYSTEMS;

EID: 33750597174     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.682222     Document Type: Conference Paper

References (37)

1. R. Acar and C. R. Vogel. Analysis of total variation penalty methods for ill-posed problems. Inverse Prob., 10:1217-1229, 1994.
2. C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro and J. Verdera, Filling-in by Joint Interpolation of Vector Fields and Grey Levels, IEEE Trans. Image Processing, 10(8), 2001, 1200-1211.
3. M. Bertalmio, A.L. Bertozzi, and G. Sapiro. Navier-Stokes, fluid dynamics, and image and video inpainting, 2001 IEEE Conference on Computer Vision and Pattern Recognition. December. Kauai, Hawaii. Available at http://www.ece.umn.edu/users/marcelo/final-cvpr.pdf.
4. M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image Inpainting, Tech. Report, ECE-University of Minnesota, 1999.
5. M. Bertalmio, L. Vese, G. Sapiro and S. Osher, Simultaneous Structure and Texture Image Inpainting, UCLA CAM Report 02-47, July 2002
6. E. J. Candès, and F. Guo. Edge-preserving Image Reconstruction from Noisy Radon Data, (Invited Special Issue of the Journal of Signal Processing on Image and Video Coding Beyond Standards.), 2001.
7. E. Candès, J. Romberg and T. Tao, Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information, Preprint: arXiv:math.GM/0409186, Sept. 2004.
8. E. Candès, and T. Tao, Near Optimal Signal Recovery From Random Projections and Universal Encoding Strategies, Preprint, submitted to IEEE Information Theory, Oct. 2004.
9. V. Caselles, R. Kimmel and G. Sapiro, On Geodesic Active Contours, Int. Journal of Computer Vision, 22(1), 1997, 61-79.
10. A. Chambolle, R. A. DeVore, N.-Y. Lee, and B. J. Lucier. Nonlinear wavelet image processing: variational problems, compression and noise removal through wavelet shrinkage. IEEE Trans. Image Processing, 7(3):319-335, 1998.
11. T. F. Chan, S. H. Kang and J. Shen, Euler's Elastica and Curvature Based inpainting, SIAM J. Appl. Math., 63(2) (2002), 564-592.
12. T. F. Chan and J. Shen, Mathematical Models for Local Non-Texture Inpainting, SIAM J. Appl. Math., 62(3) (2002), 1019-1043.
13. T. F. Chan and J. Shen, Morphologically Invariant PDE Inpaintings, UCLA CAM Report 01-15, 2001.
14. T. F. Chan, J. Shen, and H. M. Zhou, Total Variation Wavelet Inpainting, to appear in J. of Math. Imaging and Vision.
15. T. F. Chan and L. Vese, Active Contour Without Edges Submit to IEEE Tran, on Image Proc., 1998.
16. T. F. Chan and C. K. Wong, Total Variation Blind Deconvolution, IEEE Trans. Image Processing, 7 (1998), pp. 370-375.
17. T. F. Chan and H. M. Zhou, Optimal Constructions of Wavelet Coefficients Using Total Variation Regularization in Image Compression, CAM Report, No. 00-27, Dept. of Math., UCLA, July 2000.
18. L. Demanet, B. Song and T. Chan, Image Inpainting by Correspondence Maps: a Deterministic Approach, UCLA CAM Report 03-40, August 2003.
19. D. Dobson and C.R. Vogel, Convergence of An Iterative Method for Total Variation Denoising, SIAM Journal on Numerical Analysis, 34 (1997), pp. 1779-1971.
20. D. Dugatkin, H. M. Zhou, T. F. Chan and M. Effros, Lagrangian Optimization of A Group Testing for ENO Wavelets Algorithm, Proceedings to the 2002 Conference on Information Sciences and Systems, Princeton University, New Jersey, March 20-22, 2002.
21. S. Durand and J. Froment, Artifact Free Signal Denoising with Wavelets, in Proceedings of ICASSP'01, volume 6, 2001, pp. 3685-3688.
22. M. Elad, J-L. Starck, P. Querre and D. Donoho, Simultaneous Cartoon and Texture Image Inpainting Using Morphological Component Analysis (MCA), to appear in the J. on Applied and Computational Harmonic Analysis.
23. S. Esedoglu and J. Shen. Digital inpainting based on the Mumford-Shah-Euler image model. European J. Appl. Math., 13:353-370, 2002.
24. H. Igehy and L. Pereira. Image Replacement Through Texture Synthesis, Proceedings to IEEE ICIP, 1997.
25. K.-H. Jung, J.-H. Chang, and C. W. Lee, Error Concealment Technique Using Data for Block-Based Image Coding, SPIE, 2308, (1994), 1466-1477.
26. Sung Ha Kang, Tony F. Chan and Stefano Soatto, Inpainting from Multiple View, UCLA CAM Report 02-31, May 2002.
27. F. Malgouyres, Mathematical Analysis of a Model Which Combines Total Variation and Wavelet for Image Restoration, Journal of information processes, 2:1, 2002, pp 1-10.
28. F. Malgouyres and F. Guichard, Edge Direction Preserving Image Zooming: a Mathematical and Numerical Analysis, SIAM, J. Num. Anal., 39:1, 2001, pp 1-37.
29. L. Moisan, Extrapolation de Spectre et Variation Totale Ponderee, actes du GRETSI, 2001.
30. M. Masnou and J. Morel, Level-lines Based Disocclusion, IEEE ICIP, October, 1998, 259-263.
31. D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Applied. Math., 42:577-685, 1989.
32. M. Nitzberg, D. Mumford, and T. Shiota. Filtering, Segmentation, and Depth. Lecture Notes in Comp. Sci., Vol. 662. Springer-Verlag, Berlin, 1993.
33. L. Rudin, S. Osher and E. Fatemi, Nonlinear Total Variation Based Noise Removal Algorithms, Physica D, Vol 60(1992), pp. 259-268.
34. J.L. Starck, M. Elad and D. Donoho. Image Decomposition via the Combination of Sparse Representations and a Variational Approach, to appear in the IEEE Trans. Image Processing.
35. David M. Strong, Peter Blomgren, and Tony F. Chan, Spatially Adaptive Local Feature-Driven Total Variation Minimizing Image Restoration, Proceedings of SPIE, vol. 3167, 1997, pp. 222-233.
36. Y. Wang, and Q. F. Zhu, Error Control and Concealment for Video Communication: A Review, Proc. IEEE, vol 86, no. 5, pp. 974-997.
37. A. Yezzi, A. Tsai and A. Willsky, A Fully Global Approach to Image Segmentation via Coupled Curve Evolution Equations, Submitted to Journal of Visual Communication and Image Representation.