Example-driven manifold priors for image deconvolution

IEEE Transactions on Image Processing

Volumn 20, Issue 11, 2011, Pages 3086-3096

  Ni, Jie ^a,b   Turaga, Pavan ^a,b   Patel, Vishal M ^a,b   Chellappa, Rama ^a,b  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

Deconvolution; generalized cross validation (GCV); local manifold; patch manifold; regularization

Indexed keywords

BAYESIAN FRAMEWORKS; DEBLURRING PROBLEMS; DECONVOLUTION PROBLEM; GENERALIZED CROSS VALIDATION; IMAGE DATA; IMAGE DECONVOLUTION; LOCAL MANIFOLD; NATURAL IMAGES; NOISE VARIANCE; OBJECT CLASS; PATCH MANIFOLD; PRIOR INFORMATION; PRIOR KNOWLEDGE; REGULARIZATION; REGULARIZATION PARAMETERS; UNLABELED DATA;

IMAGE RECONSTRUCTION;

EID: 80054805330     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2011.2145386     Document Type: Conference Paper

References (39)

1. J. Ni, P. Turaga, V. M. Patel, and R. Chellappa, "Object dependent manifold priors for image deconvolution," in Proc. Digit. Image Processi. Anal., 2010.
2. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. New York: Winston, 1977.
3. J. Biemond, R. Lagendijk, and R. Mersereau, "Iterative methods for image deblurring," Proc. IEEE, vol. 78, no. 5, pp. 856-883, May 1990.
4. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol. 57, no. 11, pp. 1413-1457, 2004.
5. J. Kalifa, S. Mallat, and B. Roug, "Deconvolution by thresholding in mirror wavelet bases," IEEE Trans. Image Process., vol. 12, no. 4, pp. 446-457, Apr. 2003.
6. R. Neelamani, H. Choi, and R. G. Baraniuk, "Forward: Fourier-wavelet regularized deconvolution for ill-conditioned systems," IEEE Trans. Image Process., vol. 52, no. 2, pp. 418-433, Feb. 2004.
7. D. L. Donoho, "Nonlinear solution of linear inverse problems by wavelet-Vaguelette decomposition," Appl. Comput. Harmon. Anal., vol. 2, pp. 101-126, 1995.
8. V. M. Patel, G. R. Easley, and D. M. Healy, "Shearlet-based deconvolution," IEEE Trans. Image Process., vol. 18, no. 12, pp. 2673-2685, Dec. 2009.
9. M. Figueiredo, R. Nowak, and S. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 586-598, 2007.
10. M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol. 12, no. 8, pp. 906-916, Aug. 2003.
11. J.-L. Starck, M. K. Nguyen, and F. Murtagh, "Wavelets and curvelets for image deconvolution: A combined approach," Signal Process., vol. 83, no. 10, pp. 2279-2283, 2003.
12. E. J. Candès and D. L. Donoho, "Curvelets-A surprisingly effective nonadaptive representation for objects with edges," in Curves and Surface Fitting, A. Cohen, C. Rabut, and L. L. Schumaker, Eds. Nashville, TN: Vanderbilt Univ. Press, 1999.
13. M. N. Do and M. Vetterli, "The contourlet transform: An efficient directional multiresolution image representation," IEEE Trans. Image Process., vol. 14, no. 12, pp. 2091-2106, Dec. 2005.
14. A. L. Cunha, J. Zhou, and M. N. Do, "The nonsubsampled contourlet transform: Theory, design, and applications," IEEE Trans. Image Process., vol. 15, no. 10, pp. 3089-3101, Oct. 2006.
15. G. R. Easley, D. Labate, and W. Q. Lim, "Sparse directional image representations using the discrete shearlet transform," Appl. Comput. Harmon. Anal., vol. 25, no. 1, pp. 25-46, Jul. 2008.
16. M. Elad and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Trans. Image Process., vol. 15, no. 12, pp. 3736-3745, Dec. 2006.
17. J. Mairal, M. Elad, and G. Sapiro, "Sparse representation for color image restoration," IEEE Trans. Image Process., vol. 17, no. 1, pp. 53-69, Jan. 2008.
18. R. Rubinstein, A. M. Bruckstein, and M. Elad, "Dictionaries for sparse representation modeling," Proc. IEEE, vol. 98, no. 6, pp. 1045-1057, Jun. 2010.
19. W. T. Freeman, T. R. Jones, and E. C. Pasztor, "Example-based superresolution," IEEE Comput. Graph. Appl., vol. 22, no. 3, pp. 56-65, Mar. 2002.
20. "Nonlinear total variation based noise removal algorithms," Phys. D: Nonlinear Phenomena, vol. 60, no. 1-4, pp. 259-268, 1992.
21. Y. Wang, J. Yang, W. Yin, and Y. Zhang, "A new alternating minimization algorithm for total variation image reconstruction," SIAM J. Imag. Sci., vol. 1, no. 3, pp. 248-272, 2008.
22. L. He, A. Marquina, and S. Osher, "Blind deconvolution using TV regularization and Bregman iteration," Int. J. Imaging Syst. Technol., vol. 15, no. 1, pp. 74-83, 2005.
23. V. Katkovnik, K. Egiazarian, and J. Astola, "A spatially adaptive nonparametric regression image deblurring," IEEE Trans. Image Process., vol. 14, no. 10, pp. 1469-1478, Oct. 2005.
24. H. Takeda, S. Farsiu, and P. Milanfar, "Deblurring using regularized locally adaptive kernel regression," IEEE Trans. Image Process., vol. 17, no. 4, pp. 550-563, Apr. 2008.
25. G. Peyre, "Manifold models for signals and images," Comput. Vis. Image Understanding, vol. 13, no. 2, pp. 249-260, 2009.
26. P. N. Belhumeur and D. J. Kriegman, "What is the set of images of an object under all possible lighting conditions?," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., 1996, pp. 270-277.
27. D.-S. V. Tenenbaum, J. B., and J. C. Langford, "A global geometric framework for nonlinear dimensionality reduction," Science, vol. 290, no. 5500, pp. 2319-2323, Dec. 2000.
28. S. Roweis and L. Saul, "Nonlinear dimensionality reduction by locally linear embedding," Science, vol. 290, no. 5500, pp. 2323-2326, Dec. 2000.
29. A. Talwalkar, S. Kumar, and H. A. Rowley, "Large-scale manifold learning," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., 2008, pp. 1-8.
30. P. C. Hansen, J. G. Nagy, and D. P. O'Leary, Deblurring Images: Matrices, Spectra, and Filtering. Philadelphia, PA: SIAM, 2006.
31. A. Gionis, P. Indyk, and R. Motwani, "Similarity search in high dimensions via hashing," in Proc. 25th Very Large Database (VLDB) Conf., 1999, pp. 518-529.
32. M. Datar, N. Immorlica, P. Indyk, and V. S. Mirrokni, "Locality-sensitive hashing scheme based on p-stable distributions," in Proc. Symp. Computational Geometry, 2004, pp. 253-262.
33. Y. Bengio, J.-F. Paiement, P. Vincent, O. Delalleau, N. L. Roux, and M. Ouimet, "Out-of-sample extensions for LLE, ISOMAP, MDS, eigenmaps, and spectral clustering," in Proc. Neural Inf. Process. Syst. (NIPS), 2003, pp. 177-184.
34. G. H. Golub, M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics, vol. 21, no. 2, pp. 215-223, 1979.
35. N. Galatsanos and A. Katsaggelos, "Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation," IEEE Trans. Image Process., vol. 1, no. 3, pp. 322-336, Jul. 1992.
36. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. Philadelphia, PA: SIAM, 1998.
37. D. Krishnan and R. Fergus, "Fast image deconvolution using hyper- Laplacian priors," in Proc. Neural Inf. Process. Syst., Vancouver, BC, Canada, 2009, pp. 1033-1041.
38. A. Levin, Y. Weiss, F. Durand, and W. T. Freeman, "Understanding and evaluation blind deconvolution algorithms," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit. (CVPR), 2009, pp. 1964-1971.
39. R. Fergus, B. Singh, A. Hertzmann, S. T. Roweis, and W. Freeman, "Removing camera shake from a single photograph," in Proc. SIGGRAPH Conf., Boston, MA, 2006, vol. 25, pp. 787-794.