Convex generalizations of total variation based on the structure tensor with applications to inverse problems

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

Volumn 7893 LNCS, Issue , 2013, Pages 48-60

  Lefkimmiatis, Stamatios ^a   Roussos, Anastasios ^b   Unser, Michael ^a   Maragos, Petros ^c  

^a EPFL   (Switzerland)

^b QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^c NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE DIFFUSIONS; ENERGY FUNCTIONALS; IMAGE VARIATIONS; MINIMIZATION ALGORITHMS; NON-LINEAR ANISOTROPIC DIFFUSION; STRUCTURE TENSORS; TOTAL VARIATION; VECTOR-VALUED IMAGES;

EIGENVALUES AND EIGENFUNCTIONS; IMAGE ENHANCEMENT; INVERSE PROBLEMS;

TENSORS;

EID: 84884407339     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-38267-3_5     Document Type: Conference Paper

References (23)

1. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268 (1992)
2. Chan, T., Marquina, A., Mulet, P.: High-order total variation-based image restoration. SIAM J. Sci. Comput. 22, 503-516 (2000)
3. Sapiro, G.: Color snakes. Comp. Vision and Image Understanding 68(2) (1997)
4. Blomgren, P., Chan, T.: Color TV: Total Variation methods for restoration of vector-valued images. IEEE Trans. on Image Processing 7(3), 304-309 (1998)
5. Weickert, J., Schnörr, C.: A theoretical framework for convex regularizers in PDE-based computation of image motion. Int. Journ. of Computer Vision 45(3), 245-264 (2001)
6. Tschumperlé, D., Deriche, R.: Vector-valued image regularization with PDE's: A common framework for different applications. IEEE T-PAMI 27(4), 506-517 (2005)
7. Goldluecke, B., Strekalovskiy, E., Cremers, D.: The natural vectorial total variation which arises from geometric measure theory. SIAM J. Imaging Sci. 5, 537-563 (2012)
8. Sochen, N., Kimmel, R., Malladi, R.: A general framework for low level vision. IEEE Trans. on Image Processing 7, 310-338 (1998)
9. Sochen, N., Bar, L.: The Beltrami-Mumford-Shah functional. In: Scale Space and Variational Methods in Computer Vision, pp. 183-193 (2012)
10. Grasmair, M., Lenzen, F.: Anisotropic total variation filtering. Applied Mathematics & Optimization 62, 323-339 (2010)
11. Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Modeling & Simulation 7(3), 1005-1028 (2008)
12. Wetzler, A., Kimmel, R.: Efficient Beltrami flow in patch-space. In: Scale Space and Variational Methods in Computer Vision, pp. 134-143 (2012)
13. Roussos, A., Maragos, P.: Tensor-based image diffusions derived from generalizations of the total variation and Beltrami functionals. In: Proc. Int. Conf. on Image Processing (2010)
14. Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998)
15. Jähne, B.: Digital Image Processing. Springer (2002)
16. Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE T-PAMI 12(7), 629-639 (1990)
17. Catté, F., Lions, P., Morel, J., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journ. Numer. Anal. 29(1), 182-193 (1992)
18. Bhatia, R.: Matrix Analysis. Springer (1997)
19. Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 4(4), 1168-1200 (2005)
20. Lefkimmiatis, S., Ward, J., Unser, M.: Hessian Schatten-norm regularization for linear inverse problems. IEEE Trans. Image Processing 22(5), 1873-1888 (2013)
21. Rokcafellar, R.T.: Convex Analysis. Princeton Univ. Press, Princeton (1970)
22. Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Processing 18, 2419-2434 (2009)
23. 2). Soviet Math. Dokl 27, 372-376 (1983)