Total-variation based piecewise affine regularization

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

Volumn 5567 LNCS, Issue , 2009, Pages 552-564

  Yuan, Jing ^a   Schnörr, Christoph ^a   Steidl, Gabriele ^b  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONVEX DECOMPOSITION; DE-NOISING; GLOBAL OPTIMUM; PIECEWISE AFFINE FUNCTIONS; PIECEWISE AFFINES; REGULARIZER; SECOND ORDERS; TOTAL-VARIATION; VECTOR FIELDS;

COMPUTER VISION;

DECOMPOSITION;

EID: 69049106806     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02256-2_46     Document Type: Conference Paper

References (23)

1. Chambolle, A., Lions, P.L.: Image recovery via total variation minimization and related problems. Numer. Math. 76(2), 167-188 (1997)
2. Chan, T., Esedoglu, S., Park, F.E.: Image decomposition combining staicase reduction and texture extraction. J. Visual Communication and Image Representation 18(6), 468-486 (2007)
3. Chan, T., Marquina, A., Mulet, P.: Higher-order total variation-based image restoration. SIAM J. Sci. Comput. 22(2), 503-516 (2000)
4. Danielsson, P.E., Lin, Q.: Efficient detection of second-degree variations in 2D and 3D images. J. Vis. Comm. Image Repr. 12, 255-305 (2001)
5. Didas, S., Setzer, S., Steidl, G.: Combined -2 data and gradient fitting in conjunction with -1 regularization. Advances in Computational Mathematics 30(1), 79-99 (2009)
6. Girault, V., Raviart, P.-A.: Finite Element Methods for Navier-Stokes Equations. Springer, Heidelberg (1986)
7. Goldstein, D., Osher, S.: The Split Bregman method for l1 regularized problems. UCLA CAM Report (2008)
8. Hintermüller, W., Kunisch, K.: Total bounded variation regularization as a bilaterally constraint optimization problem. SIAM J. Appl. Math. 64(4), 1311-1333 (2004)
9. Hyman, J.M., Shashkov, M.: Natural discretizations for the divergence, gradient, and curl on logically rectangular grids. Comput. Math. Appl. 33(4), 81-104 (1997)
10. Hyman, J.M., Shashkov, M.: Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids. Appl. Numer. Math. 25(4), 413-442 (1997)
11. 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 Processing 12(12), 1579-1590 (2003)
12. Lysaker, M., Tai, X.C.: Iterative image restoration combining total variation minimization and a second-order functional. International Journal of Computer Vision 66(1), 5-18 (2006)
13. Rahman, T., Tai, X.C., Osher, S.J.: A TV-stokes denoising algorithm. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 473-483. Springer, Heidelberg (2007)
14. Rockafellar, R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. 1(2), 97-116 (1976)
15. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268 (1992)
16. Scherzer, O.: Denoising with higher order derivatives of bounded variation and an application to parameter estimation. Computing 60, 1-27 (1998)
17. Setzer, S.: Split Bregman algorithm, Douglas-Rachford splitting and frame shrinkage. In: Lie, K.A., Lysaker, M., Morken, K., Tai, X.C. (eds.) Scale Space and Variational Methods. LNCS. Springer, Heidelberg (2009)
18. Trobin, W., Pock, T., Cremers, D., Bischof, H.: An unbiased second-order prior for high-accuracy motion estimation. In: Rigoll, G. (ed.) DAGM2008. LNCS, vol. 5096, pp. 296-405. Springer, Heidelberg (2008)
19. Vogel, C.R.: Computational Methods for Inverse Problems. SIAM, Philadelphia (2002)
20. You, Y.L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Processing 9(10), 1723-1730 (2000)
21. Yuan, J., Schnörr, C., Steidl, G.: Simultaneous optical flow estimation and decomposition. SIAM J. Scientific Computing 29(6), 2283-2304 (2007)
22. Yuan, J., Schnörr, C., Memin, E.: Discrete orthogonal decomposition and variational fluid flow estimation. J. Math. Imaging and Vision 28(1), 67-80 (2007)
23. Yuan, J., Schnörr, C., Steidl, G.: Convex hodge decomposition and regularization of image flows. J. Math. Imag. Vision 33(2), 169-177 (2009)