Recovering piecewise smooth multichannel images by minimization of convex functionals with total generalized variation penalty

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 8293 LNCS, Issue , 2014, Pages 44-77

  Bredies, Kristian ^a  

^a UNIVERSITY OF GRAZ   (Austria)

Author keywords

Compressive imaging; Dequantization; Image deblurring; Image denoising; Multichannel images; Primal dual algorithms; Total generalized variation; Zooming

Indexed keywords

ALGORITHMS; GLOBAL OPTIMIZATION; IMAGE DENOISING;

COMPRESSIVE IMAGING; DEQUANTIZATION; GENERALIZED VARIATION; IMAGE DEBLURRING; MULTICHANNEL IMAGES; PRIMAL DUAL ALGORITHMS; ZOOMING;

IMAGE ENHANCEMENT;

EID: 84958538694     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-54774-4_3     Document Type: Conference Paper

References (37)

1. Alberti, G., Bouchitté, G., Maso, D.D.: The calibration method for the Mumford-Shah functional and free-discontinuity problems. Calc. Var. Partial Differ. Equ. 16(3), 299-333 (2003)
2. Bredies, K., Dong, Y., Hinterm̈uller, M.: Spatially dependent regularization parameter selection in total generalized variation models for image restoration. Int. J. Comput. Math. 90(1), 109-123 (2013)
3. Bredies, K., Holler, M.: A total variation-based JPEG decompression model. SIAM J. Imaging Sci. 5(1), 366-393 (2012)
4. Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAM J. Imaging Sci. 3, 492-526 (2011)
5. Bredies, K., Valkonen, T.: Inverse problems with second-order total generalized variation constraints. In: Proceedings of SampTA 2011, 9th International Conference on Sampling Theory and Applications (2011)
6. Bredies, K., Holler, M.: Artifact-free JPEG decompression with total generalized variation. In: VISAPP 2012: Proceedings of the International Conference on Computer Vision Theory and Applications (2012)
7. Bresson, X., Chan, T.F.C.: Fast dual minimization of the vectorial total variation norm and applications to color image processing. Inverse Probl. Imaging 2(4), 455-484 (2008)
8. Chambolle, A., Lions, P.L.: Image recovery via total variation minimization and related problems. Numer. Math. 76, 167-188 (1997)
9. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120-145 (2011)
10. Chan, T.F., Esedoglu, S., Park, F.E.: Image decomposition combining staircase reduction and texture extraction. J. Visual Commun. Image Represent. 18(6), 464-486 (2007)
11. Dong, Y., Hintermüller, M., Rincon-Camacho, M.: Automated regularization parameter selection in multi-scale total variation models for image restoration. J. Math. Imaging Vis. 40, 82-104 (2011)
12. Duarte, M.F., Davenport, M.A., Takhar, D., Laska, J., Sun, T., Kelly, K., Bara-niuk, R.G.: Single-pixel imaging via compressive sampling. IEEE Signal Proc. Mag. 25(2), 83-91 (2008)
13. Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293-318 (1992)
14. Hinterberger, W., Scherzer, O.: Variational methods on the space of functions of bounded Hessian for convexification and denoising. Computing 76, 109-133 (2006)
15. ina@Flickr: Alina's eye. Licenced under CreativeCommons-by-2.0 (http://creativecommons.org/licenses/by/2.0/). http://www.flickr.com/photos/ angelina/3201337190 (2009)
16. Klöckner, A.: PyCUDA 2011.2.2. http://mathema.tician.de/software/ pycuda
17. Kubina, J.: Bubble popper. Licenced under CreativeCommons-by-sa-2.0 (http://creativecommons.org/licenses/by-sa/2.0/). http://www.flickr.com/photos/ kubina/42275122 (2005)
18. Lions, P.L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16(6), 964-979 (1979)
19. Lysaker, M., Lundervold, A., Tai, X.C.: Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans. Image Process. 12, 1579-1590 (2003)
20. Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577-685 (1989)
21. Nikolova, M.: Local strong homogeneity of a regularized estimator. SIAM J. Appl. Math. 61(2), 633-658 (2000)
22. NIVIDA Corporation: CUDA toolkit 4.0. http://www.nvidia.com/getcuda
23. Papafitsoros, K., Schönlieb, C.B.: A combined first and second order variational approach for image reconstruction. ArXiv e-print 1202.6341 (2012)
24. Pock, T., Cremers, D., Bischof, H., Chambolle, A.: An algorithm for minimizing the Mumford-Shah functional. In: IEEE 12th International Conference on Computer Vision (ICCV). pp. 1133-1140 (2009)
25. Python Software Foundation: Python programming language 2.6. http://www. python.org/
26. Rice Single-Pixel Camera Project: CS camera data. http://dsp.rice.edu/ cscamera
27. Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14(5), 877-898 (1976)
28. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268 (1992)
29. Schristia@Flickr: 1, 2, 3. Licenced under CreativeCommons-by-2.0 (http://creativecommons.org/licenses/by/2.0/). http://www.flickr.com/photos/ schristia/4057490235 (2009)
30. Stampacchia, G.: Le probl̀eme de Dirichlet pour les équations elliptiques du second ordre ̀a coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15(1), 189-258 (1965)
31. Steve-h@Flickr: Wet green smiles. Licenced under CreativeCommons-by-sa-2. 0 (http://creativecommons.org/licenses/by-sa/2.0/). http://www.flickr.com/ photos/sbh/3859041020 (2009)
32. Steve-h@Flickr: Oak leaves and bokeh. Licenced under CreativeCommons-by- sa-2.0 (http://creativecommons.org/licenses/by-sa/2.0/). http://www.flickr.com/ photos/sbh/6802942537 (2012)
33. Temam, R.: Mathematical Problems in Plasticity. Bordas, Paris (1985)
34. The Scipy Community: Scientific tools for Python. http://www.scipy.org/
35. Vese, L.: A study in the BV space of a denoising-deblurring variational problem. Appl. Math. Opt. 44, 131-161 (2001)
36. Ring, W.: Structural properties of solutions to total variation regularization problems. ESAIM: Math. Model. Num. 34(4), 799-810 (2000)
37. Yang, J., Yin, W., Zhang, Y., Wang, Y.: A fast algorithm for edge-preserving variational multichannel image restoration. SIAM J. Imaging Sci. 2(2), 569-592 (2009)