A guide to the TV zoo

Lecture Notes in Mathematics

Volumn 2090, Issue , 2013, Pages 1-70

  Burger, Martin ^a   Osher, Stanley ^b  

^a UNIVERSITY OF MÜNSTER   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84887418913     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-319-01712-9_1     Document Type: Article

References (205)

1. J.F. Abascal, J. Chamorro-Servent, J. Aguirre, J.J. Vaquero, S. Arridge, T. Correia, J. Ripoll, M. Desco, Fluorescence diffuse optical tomography using the split Bregman method. Med. Phys. 38, 6275 (2011)
2. R. Acar, C.R. Vogel, Analysis of total variation penalty methods. Inverse Probl. 10, 1217-1229 (1994)
3. G. Adde, M. Clerc, R. Keriven, Imaging methods for MEG/EEG inverse problem. Int. J. Bioelectromagn. 7, 111-114 (2005)
4. A. Almansa, V. Caselles, G. Haro B. Rouge, Restoration and zoom of irregularly sampled, blurred and noisy images by accurate total variation minimization with local constraints. Multiscale Mod. Simulat. 5, 235-272 (2006)
5. L. Ambrosio, V. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via-convergence. Comm. Pure Appl. Math. 43, 999-1036 (1990)
6. L. Ambrosio, N. Fusco, D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems (Oxford University Press, Oxford, 2000)
7. F. Andreu, C. Ballester, V. Caselles, J.M. Mazon, Minimizing total variation flow. Differ. Integr. Equat. 14, 321-360 (2001)
8. F. Andreu, C. Ballester, V. Caselles, J.M. Mazon, The Dirichlet problem for the total variation flow. J. Funct. Anal. 180, 347-403 (2001)
9. F. Andreu, V. Caselles, J.I. Diaz, J.M. Mazon, Some qualitative properties for the total variation flow. J. Funct. Anal. 188, 516-547 (2002)
10. U. Ascher, E. Haber, Computational Methods for Large Distributed Parameter Estimation Problems with Possible Discontinuities. Symp. Inverse Problems, Design and Optimization, Rio, 2004
11. P. Athavale, E. Tadmor, Multiscale image representation using integro-differential equations. Inverse Probl. Imag. 3, 693-710 (2009)
12. G. Aubert, J.F. Aujol, Modeling very oscillating signals, application to image processing. Appl. Math. Optim. 51, 163-182 (2005)
13. G. Aubert, J.F. Aujol, A Variational approach to remove multiplicative noise. SIAM J. Appl. Math. 68, 925-946 (2008)
14. J.F. Aujol, Some first-order algorithms for total variation based image restoration. J. Math. Imag. Vis. 34, 307-327 (2009)
15. J.F. Aujol, A. Chambolle, Dual norms and image decomposition models. IJCV 63, 85-104 (2005)
16. J.F. Aujol, G. Aubert, L. Blanc-Feraud, A. Chambolle, Image decomposition into a bounded variation component and an oscillating component. J. Math. Imag. Vis. 22, 71-88 (2005)
17. J.F. Aujol, G. Gilboa, T. Chan, S. Osher, Structure-texture image decomposition-modeling, algorithms, and parameter selection. Int. J. Comput. Vis. 67, 111-136 (2006)
18. W. Baatz, M. Fornasier, P. Markowich, C.B. Schönlieb, Inpainting of ancient Austrian frescoes. Conference Proceedings of Bridges 2008, Leeuwarden, 2008, pp. 150-156
19. S.D. Babacan, R. Molina, A.K. Katsaggelos, Variational Bayesian blind deconvolution using a total variation prior. IEEE Trans. Image Proc. 18, 12-26 (2009)
20. M. Bachmayr, Iterative Total Variation Methods for Nonlinear Inverse Problems, Master Thesis (Johannes Kepler University, Linz, 2007)
21. M. Bachmayr, M. Burger, Iterative total variation methods for nonlinear inverse problems. Inverse Probl. 25, 105004 (2009)
22. C. Ballester, V. Caselles, L. Igual, J. Verdera, B. Rouge, A variational model for PCXS image fusion. IJCV 69, 43-58 (2006)
23. J. Bardsley, A. Luttman, Total variation-penalized Poisson likelihood estimation for ill-posed problems . Adv. Comp. Math. 31, 35-59 (2009)
24. C. Bazan, PDE-Based Image and Structure Enhancement for Electron Tomography of Mitochondria, PhD-Thesis (San Diego State University, San Diego, 2009)
25. G. Bellettini, V. Caselles, The total variation flow in RN . J. Differ. Equat. 184, 475-525 (2002)
26. G. Bellettini, V. Caselles, M. Novaga, Explicit solutions of the eigenvalue problem-div .Du=jDuj/D u. SIAM J. Math. Anal. 36, 1095-1129 (2005)
27. M. Benning, Singular Regularization of Inverse Problems (PhD Thesis, WWU Münster, 2011)
28. M. Benning, M. Burger, Error estimation with general fidelities. Electron. Trans. Numer. Anal. 38, 44-68 (2011)
29. M. Benning, C. Brune, M. Burger, J. Müller, Higher-order TV methods-enhancement via Bregman iteration. J. Sci. Comput. 54(2-3), 269-310 (2013)
30. B. Berkels, M. Burger, M. Droske, O. Nemitz, M. Rumpf, Cartoon extraction based on anisotropic image classification, in Vision, Modeling, and Visualization 2006: Proceedings, ed. by L. Kobbelt, T. Kuhlen, T. Aach, R. Westerman (IOS Press, Aachen, 2006)
31. J.M. Bioucas-Dias, M.A.T. Figueiredo, J.P. Oliveira, Total variation-based image deconvolution: a majorization-minimization approach, in 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings, vol. 2, pp. II, 14-19 May 2006
32. K.T. Block, M. Uecker, J. Frahm, Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint. Magn. Reson. Med. 57, 1086-1098 (2007)
33. P. Blomgren, T. Chan, Color TV: Total variation methods for restoration of vector valued images. IEEE Trans. Image Proc. 7, 304-309 (1998)
34. T. Bonesky, K.S. Kazimierski, P. Maass, F. Schöpfer, T. Schuster, Minimization of Tikhonov functionals in Banach spaces. Abstr. Appl. Anal. 19, 192679 (2008)
35. S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3, 1-122 (2011)
36. K. Bredies, K. Kunisch, T. Pock, Total generalized variation. SIAM J. Imag. Sci. 3, 492-526 (2010)
37. L.M. Bregman, The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comp. Math. Math. Phys. 7, 200-217 (1967)
38. M. Breuss, T. Brox, A. Bürgel, T. Sonar, J. Weickert, Numerical aspects of TV flow. Numer. Algorithms 41, 79-101 (2006)
39. A. Briani, A. Chambolle, M. Novaga, G. Orlandi, On the gradient flow of a one-homogeneous functional, Preprint (SNS, Pisa, 2011)
40. T. Brox, J. Weickert, A TV flow based local scale measure for texture discrimination, in Computer Vision-ECCV 2004, ed. by T. Pajdla, J. Matas (Springer, Berlin, 2004), pp. 578-590
41. T. Brox, M. Welk, G. Steidl, J. Weickert, Equivalence results for TV diffusion and TV regularization, in Scale Space Methods in Computer Vision, ed. by L.D. Griffin, M. Lillholm (Springer, Berlin, 2003), pp. 86-100
42. C. Brune, A. Sawatzky, M. Burger, Bregman-EM-TV methods with application to optical nanoscopy, in Proceedings of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision. LNC, vol. 5567 (Springer, Berlin, 2009), pp. 235-246
43. C. Brune, H. Maurer, M.Wagner, Detection of intensity and motion edges within optical flow via multidimensional control. SIAM J. Imag. Sci. 2, 1190-1210 (2009)
44. C. Brune, A. Sawatzky, M. Burger, Primal and dual Bregman methods with application to optical nanoscopy. Int. J. Comput. Vis. 92, 211-229 (2011)
45. A. Buades, B. Coll, J.M. Morel, A review of image denoising algorithms, with a new one. Multiscale Model. Simulat. 4, 490-530 (2005)
46. M. Burger, M. Hintermüller, Projected gradient flows for BV/level set relaxation . PAMM 5, 11-14 (2005)
47. M. Burger, S. Osher, Convergence rates of convex variational regularization. Inverse Probl. 20, 1411-1421 (2004)
48. M. Burger, O. Scherzer, Regularization methods for blind deconvolution and blind source separation problems. Math. Contr. Signals Syst. 14, 358-383 (2001)
49. M. Burger, G. Gilboa, S. Osher, J. Xu, Nonlinear inverse scale space methods for image restoration. Comm. Math. Sci. 4, 179-212 (2006)
50. M. Burger, E. Resmerita, L. He, Error estimation for Bregman iterations and inverse scale space methods. Computing 81, 109-135 (2007)
51. M. Burger, K. Frick, S. Osher, O. Scherzer, Inverse total variation flow. SIAM Multiscale Mod. Simul. 6, 366-395 (2007)
52. M. Burger, L. He, C.B. Schönlieb, Cahn-Hilliard inpainting and a generalization for grayvalue images. SIAM J. Imag. Sci. 2, 1129-1167 (2009)
53. M. Burger, M. Möller, M. Benning, S. Osher, An adaptive inverse scale space method for compressed sensing. Math. Comput. (2012, to appear)
54. M. Burger, M. Franek, C.-B. Schönlieb, Regularized regression and density estimation based on optimal transport. Appl. Math. Res. Express 2012, 209-253 (2012)
55. J. Cai, S. Osher, Z. Shen, Linearized Bregman iterations for compressed sensing. Math. Comput. 78, 1515-1536 (2008)
56. J. Cai, S. Osher, Z. Shen, Convergence of the linearized Bregman iteration for l1-norm minimization. Math. Comput. 78, 2127-2136 (2009)
57. J. Cai, S. Osher, Z. Shen, Linearized Bregman iteration for frame based image deblurring. SIAM J. Imag. Sci. 2, 226-252 (2009)
58. V. Caselles, A. Chambolle,M. Novaga, The discontinuity set of solutions of the TV denoising problem and some extensions. MMS 6, 879-894 (2007)
59. V. Caselles, A. Chambolle, M. Novaga, Regularity for solutions of the total variation denoising problem. Rev. Mat. Iberoamericana 27, 233-252 (2011)
60. A. Chambolle, An algorithm for total variation regularization and denoising. J. Math. Imag. Vis. 20, 89-97 (2004)
61. A. Chambolle, P.L. Lions, Image recovery via total variational minimization and related problems. Numer. Math. 76, 167-188 (1997)
62. A. Chambolle, R. DeVore, N.Y. Lee, B. Lucier, Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage. IEEE Trans. Image Proc. 7, 319-335 (1998)
63. A. Chambolle, V. Caselles, D. Cremers,M. Novaga, T. Pock, An Introduction to total variation for image analysis, in Theoretical Foundations and Numerical Methods for Sparse Recovery, ed. by M. Fornasier. Radon Series in Applied and Computational Mathematics (De Gruyter, Berlin, 2010)
64. T. Chan, J. Shen, Mathematical models for local non-texture inpainting. SIAM J. Appl. Math. 62, 1019-1043 (2001)
65. T. Chan, J. Shen, Image Processing and Analysis (SIAM, Philadelphia, 2005)
66. T. Chan, L.A. Vese, Active contours without edges. IEEE Trans. Image Process. 10, 266-277 (2001)
67. T. Chan, C.W. Wong, Total variation blind deconvolution. IEEE Trans. Imag. Proc. 7, 370-375 (1998)
68. T. Chan, A. Marquina, P. Mulet, Second order differential functionals in total variation-based image restoration. CAM Report 98-35, UCLA, 1998
69. T. Chan, S.H. Kang, J. Shen, Total variation denoising and enhancement of color images based on the CB and HSV color models. J. Vis. Comm. Image Represent. 12, 422-435 (2001)
70. T.F. Chan, S. Esedoglu, Aspects of total variation regularized L1 function approximation. SIAM J. Appl. Math. 65, 1817-1837 (2005)
71. T.F. Chan, S. Esedoglu, M. Nikolova, Algorithms for finding global minimizers of denoising and segmentation models. SIAM J. Appl. Math. 66, 1632-1648 (2006)
72. G. Chavent, K. Kunisch, Regularization of linear least squares problems by total bounded variation. ESAIM Cont. Optim. Calc. Var. 2, 359-376 (1997)
73. O. Christiansen, T.-M. Lee, J. Lie, U. Sinha, T.F. Chan, Total variation regularization of matrix-valued images. Int. J. Biomed. Imaging 2007, Article ID 27432, 11 p. (2007). doi:10.1155/2007/27432
74. L. Cinque, G. Morrone, Retinex vombined with total variation for image illumination normalization, in Image Analysis and Processing U ICIAP 2009. LNCS, vol. 5716 (Springer, Berlin, 2009), pp. 958-964
75. S. Comelli, A Novel Class of Priors for Edge-Preserving Methods in Bayesian Inversion. Master thesis, University of Milano, 2011
76. R. Deriche, P. Kornprobst, G. Aubert, Optical flow estimation while preserving its discontinuities: A variational approach, in Proceedings of the Asian Conference on Computer Vision, ACCVŠ95, Singapore, 1995
77. N. Dey, L. Blanc-Feraud, C. Zimmer, Z. Kam, P. Roux, J.C. Olivo-Marin, J. Zerubia, Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution. Microsc. Res. Tech. 69, 260-266 (2006)
78. D. Dobson, O. Scherzer, Analysis of regularized total variation penalty methods for denoising. Inverse Probl. 12, 601-617 (1996)
79. D. Donoho, I. Johnstone, Ideal spatial adaptation via wavelet shrinkage. Biometrika 81, 425-455 (1994)
80. A. Douiri, M. Schweiger, J. Riley, S.R. Arridge, Local diffusion regularisation method for optical tomography reconstruction using robust statistics. Optic. Lett. 30, 2439-2441 (2005)
81. I. Ekeland, R. Temam, Convex Analysis and Variational Problems. Corrected Reprint Edition (SIAM, Philadelphia, 1999)
82. H.W. Engl, M. Hanke, A. Neubauer, Regularization of Inverse Problems (Kluwer, Dordrecht, 1996)
83. S. Esedoglu, S.J. Osher, Decomposition of images by the anisotropic Rudin-Osher-Fatemi model. Comm. Pure Appl. Math. 57, 1609-1626 (2004)
84. E. Esser, Primal Dual Algorithms for Convex Models and Applications to Image Restoration, Registration and Nonlocal Inpainting. PhD thesis, UCLA, 2010
85. E. Esser, X. Zhang, T. Chan, A general framework for a class of first order primal-dual algorithms for tv minimization. SIAM J. Imag. Sci. 3, 1015-1046 (2010)
86. L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions (CRC Press, Boca Raton, 1992)
87. X. Feng, A. Prohl, Analysis of total variation flow and its finite element approximations. ESAIM: Math. Mod. Numer. Anal. 37, 533-556 (2003)
88. J. Flemming, B. Hofmann, Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities. Inverse Probl. 27, 085001 (2011)
89. M. Fornasier, Mathematics enters the picture, in Mathknow Mathematics, ed. by M. Emmer, A. Quarteroni. Applied Sciences and Real Life (Springer, Milan, 2009), pp. 217-228
90. M. Fornasier, G. Teschke, R. Ramlau, A comparison of joint sparsity and total variation minimization algorithms in a real-life art restoration problem. Adv. Comput. Math. 31, 301-329 (2009)
91. M. Freiberger, C. Clason, H. Scharfetter, Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach. Appl. Optic. 49, 3741-3747 (2010)
92. M.A. Freitag, N.K. Nichols, C.J. Budd, Resolution of sharp fronts in the presence of model error in variational data assimilation, Preprint (University of Bath, 2010)
93. H.Y. Gao, A.G. Bruce, WaveShrink with firm shrinkage. Statist. Sinica 7, 855-874 (1997)
94. S. Geman, D. Geman, Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741 (1984)
95. E. Giusti, Minimal Surfaces and Functions of Bounded Variation (Birkhäuser, Boston, 1984)
96. T. Goldstein, S. Osher, The split Bregman method for L1 regularized problems. SIAM J. Imag. Sci. 2, 323-343 (2009)
97. B. Goris, M.W. Van den Broek, K.J. Batenburg, H.H. Mezerji, S. Bals, Electron tomography based on a total variation minimization reconstruction technique. Ultramicroscopy 113, 120-130 (2012)
98. M. Grasmair, Generalized Bregman distances and convergence rates for non-convex regularization methods. Inverse Probl. 26, 115014 (2010)
99. M. Grasmair, Linear convergence rates for Tikhonov regularization with positively homogeneous functionals. Inverse Probl. 27, 075014 (2011)
100. A. Haddad, Y.Meyer, Variational Methods in Image Processing. CAM-Report 04-52, UCLA, 2004
101. A. Haddad, Texture separation in BV-G and BV-L1 models. SIAM Multiscale Model. Simul. 6, 273-286 (2007)
102. L. He, A. Marquina, S. Osher, Blind deconvolution using TV regularization and Bregman iteration. Int. J. Imag. Syst. Tech. 15, 74-83 (2005)
103. L. He, T.C. Chung, S. Osher, T. Fang, P. Speier, MR Image Reconstruction by Using the Iterative Refinement Method and Nonlinear Inverse Scale Space Methods. CAM Report 06-35, UCLA, 2005
104. L. He, M. Burger, S. Osher, Iterative total variation regularization with non-quadratic fidelity. J. Math. Imag. Vis. 26, 167-184 (2006)
105. W. Hinterberger, O. Scherzer, Variational methods on the space of functions of bounded Hessian for convexification and denoising. Computing 76, 109-133 (2006)
106. M. Hintermüller, M. Monserrat Rincon-Camacho, Expected absolute value estimators for a spatially adapted regularization parameter choice rule in L1-TV-based image restoration. Inverse Probl. 26, 085005 (2010)
107. B. Hofmann, B. Kaltenbacher, C. Pöschl, O. Scherzer, A Convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Inverse Probl. 23, 987-1010 (2007)
108. Y.M. Huang, M.K. Ng, Y.W. Wen, A new total variation method for multiplicative noise Removal. SIAM J. Imag. Sci. 2, 20-40 (2009)
109. P.J. Huber, Robust estimation of a location parameter. Ann. Math. Stat. 35, 73-101 (1964)
110. J. Idier, Bayesian Approach to Inverse Problems (Wiley, New York, 2008)
111. M.D. Iordache, J.M. Bioucas-Dias, A. Plaza, Total variation regulatization in sparse hyperspectral unmixing, in 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (IEEE, New York, 2011), pp. 1-4
112. Z. Jin, X. Yang, A variational model to remove the multiplicative noise in ultrasound images. J. Math. Imag. Vis. 74, 39-62 (2011)
113. E. Jonsson, S.C. Huang, T. Chan, Total Variation Regularization in Positron Emission Tomography. CAM Report 98-48, UCLA, 1998
114. J.P. Kaipio, E. Somersalo, Statistical and Computational Inverse Problems (Springer, New York, 2004)
115. S. Keeling, C. Clason, M. Hintermüller, F. Knoll, A. Laurain, G. Winckel, An image space approach to Cartesian based parallel MR imaging with total variation regularization. Med. Image Anal. 16, 189-200 (2012)
116. S. Kindermann, S. Osher, P.W. Jones, Deblurring and denoising of images by nonlocal functionals. Multiscale Model. Simul. 4, 1091-1115 (2005)
117. S. Kindermann, S. Osher, J. Xu, Denoising by BV-duality. J. Sci. Comp. 28, 411-444 (2006)
118. F. Knoll, M. Unger, C. Clason, C. Diwoky, T. Pock, R. Stollberger, Fast reduction of undersampling artifacts in radial MR angiography with 3D total variation on graphics hardware. Magn. Reson. Mater. Phy. 23, 103-114 (2010)
119. F. Knoll, K. Bredies, T. Pock, R. Stollberger, Second order total generalized variation (TGV) for MRI. Magn. Reson. Med. 65, 480-491 (2011)
120. F. Knoll, C. Clason, K. Bredies, M. Uecker, R. Stollberger, Parallel imaging with nonlinear reconstruction using variational penalties. Magn. Reson. Med. 67, 34-41 (2012)
121. M. Lassas, S. Siltanen, Can one use total variation prior for edge preserving Bayesian inversion. Inverse Probl. 20, 1537-1564 (2004)
122. P. Lax, Functional Analysis (Wiley, New York, 2002)
123. T. Le, R. Chartrand, T.J. Asaki, A variational approach to reconstructing images corrupted by Poisson noise. J. Math. Imag. Vis. 27, 257-263 (2007)
124. J. Lellman, J. Kappes, J. Yuan, F. Becker, C. Schnörr, Convex multi-class image labeling by simplex-constrained total variation Technical report (University of Heidelberg, 2008)
125. C. Lemarechal, C. Sagastizabal, Practical aspects of the Moreau-Yosida regularization: theoretical preliminaries. SIAM J. Optim. 7 367-385 (1997)
126. J. Lie, J.M. Nordbotten, Inverse scale spaces for nonlinear regularization. J. Math. Imag. Vis. 27, 41-50 (2007)
127. D.A. Lorenz, Convergence rates and source conditions for Tikhonov regularization with sparsity constraints. J. Inverse Ill-Posed Probl. 16, 463-478 (2008)
128. Y. Lou, X. Zhang, S. Osher, A. Bertozzi, Image recovery via nonlocal operators. J. Sci. Comput. 42, 185-197 (2010)
129. C. Louchet, Modeles variationnels et Bayesiens pour le d'ebruitage d'images: de la variation totale vers les moyennes non-locales. PhD thesis, University Paris-Descartes, 2008
130. C. Louchet, L.Moisan, Total Variation as a local filter. SIAM J. Imag. Sci. 4, 651-694 (2011)
131. R. Luce, S. Perez, Parameter identification for an elliptic partial differential equation with distributed noisy data. Inverse Probl. 15, 291-307 (1999)
132. M. Lustig, D.L. Donoho, J.M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58, 1182-1195 (2007)
133. W. Ma, S. Osher, A TV Bregman Iterative Model of Retinex Theory. CAM-Report 10-13, UCLA, 2010
134. Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations (AMS, Providence, 2001)
135. G. Mohler, A. Bertozzi, T. Goldstein, S. Osher, Fast TV regularization for 2D maximum penalized likelihood estimation. J. Comput. Graph. Stat. 20, 479-491 (2011)
136. M. Möller, A Variational Approach for Sharpening High-Dimensional Images. Diploma thesis, WWU Münster, 2009
137. M. Möller, T. Wittman, A. Bertozzi, M. Burger, A variational approach for sharpening highdimensional images. SIAM J. Imag. Sci. 5, 150-178 (2012)
138. J.M. Morel, S. Solimini, Variational Methods for Image Segmentation (Birkhäuser, Boston, 1995)
139. J. Müller, Parallel Total Variation Minimization. Diploma thesis, WWU Münster, 2008
140. D. Mumford, J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577-685 (1989)
141. F. Natterer, F. Wübbeling, Mathematical Methods in Image Reconstruction (SIAM, Philadelphia, 2001)
142. M.K. Ng,W.Wang, A total variation model for retinex. SIAM J. Imag. Sci. 4, 345-365 (2011)
143. A. Obereder, S. Osher, O. Scherzer, On the use of dual norms in bounded variation type regularization, in Properties from Incomplete Data, ed. by R. Klette et al. (Kluwer, Dordrecht, 2005), pp. 373-390
144. A. Obereder, O. Scherzer, A. Kovac, Bivariate density estimation using BV regularisation. Comput. Stat. Data Anal. 51, 5622-5634 (2007)
145. S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, New York, 2002)
146. S. Osher, O. Scherzer, G-norm properties of bounded variation regularization. Comm. Math. Sci. 2, 237-254 (2004)
147. S. Osher, A. Sole, L. Vese, Image decomposition and restoration using total variation minimization and the H-1 norm. SIAM Multiscale Model. Simul. 1, 349-370 (2003)
148. S. Osher, M. Burger, D. Goldfarb, J. Xu, W. Yin, An iterative regularization method for total variation based image restoration. Multiscale Model. Simul. 4, 460-489 (2005)
149. Y. Pan, R.T. Whitaker, A. Cheryauka, D. Ferguson, TV-regularized iterative image reconstruction on a mobile C-ARM CT, in Proceedings of SPIE Medical Imaging 2010, vol. 7622 (SPIE, San Diego, 2010)
150. V.Y. Panin, G.L. Zeng, G.T. Gullberg, Total variation regulated EM Algorithm. IEEE Trans. Nucl. Sci. NS-46, 2202-2010 (1999)
151. E. Pantin, J.L. Starck, F. Murtagh, Deconvolution and blind deconvolution in astronomy, in Blind Image Deconvolution: Theory and Applications, ed. by K. Egiazarian, P. Campisi (CRC Press, Boca Raton, 2007), pp. 277-317
152. K.D. Paulsen, H. Jiang, Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization. Appl. Opt. 35, 3447-3458 (1996)
153. M. Persson, D. Bone, H. Elmqvist, Total variation norm for three-dimensional iterative reconstruction in limited view angle tomography. Phys. Med. Biol. 46, 853-866 (2001)
154. G. Peyre, S. Bougleux, L. Cohen, Non-local regularization of inverse problems, in Proceedings of the 10th European Conference on Computer Vision. LNCS, vol. 5304 (Springer, Berlin, 2008), pp. 57-68
155. T. Pock, A. Chambolle, H. Bischof, D. Cremers, A convex relaxation approach for computing minimal partitions, in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2009
156. T. Pock, D. Cremers, H. Bischof, A. Chambolle, Global solutions of variational models with convex regularization. SIAM J. Imag. Sci. 3, 1122-1145 (2010)
157. T. Pock, A. Chambolle, D. Cremers, H. Bischof, A convex relaxation approach for computing minimal partitions, in IEEE Conference on Computer Vision and Pattern Recognition, 2009. CVPR 2009, 20-25 June 2009 (2009), pp. 810-817. doi:10.1109/CVPR.2009.5206604
158. Z. Qin, D. Goldfarb, S. Ma, An Alternating Direction Method for Total Variation Denoising, Preprint (Columbia University, 2011)
159. S. Remmele, M. Seeland, J. Hesser, Fluorescence microscopy deconvolution based on Bregman iteration and Richardson-Lucy algorithm with TV regularization, in Proceedings of the Workshop: Bildverarbeitung fï£iur die Medizin 2008 (Springer, Berlin, 2008), pp. 72-76
160. E. Resmerita, Regularization of ill-posed problems in Banach spaces: convergence rates. Inverse Probl. 21, 1303-1314 (2005)
161. E. Resmerita, O. Scherzer, Error estimates for non-quadratic regularization and the relation to enhancing. Inverse Probl. 22, 801-814 (2006)
162. W. Ring, Structural properties of solutions to total variation regularization problems. Math. Model. Numer. Anal. 34, 799-810 (2000)
163. L.I. Rudin, S.J. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268 (1992)
164. L. Rudin, P.L. Lions, S. Osher, Multiplicative denoising and debluring: theory and algorithms, in Geometric Level Sets in Imaging, Vision, and Graphics, ed. by S. Osher, N. Paragios (Springer, New York, 2003), pp. 103-119
165. A. Sawatzky, C. Brune, F. Wübbeling, T. Kösters, K. Schäfers, M. Burger, Accurate EMTV algorithm in PET with low SNR, 2008. IEEE Nuclear Science Symposium Conference Record. doi: 10.1109/NSSMIC.2008. 4774392
166. A. Sawatzky, (Nonlocal) Total Variation in Medical Imaging. PhD thesis, WWU Münster, 2011
167. A. Sawatzky, C. Brune, J. Müller, M. Burger, Total variation processing of images with Poisson statistics, in Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns, LNCS, vol. 5702 (Springer, Berlin, 2009), pp. 533-540
168. A. Sawatzky, D. Tenbrinck, X. Jiang, M. Burger, A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models. CAM Report 11-81, UCLA, 2011
169. O. Scherzer, C. Groetsch, Inverse scale space theory for inverse problems, in Scale-Space and Morphology in Computer Vision. Proceedings of the third International Conference Scalespace 2001, ed. by M. Kerckhove (Springer, Berlin, 2001), pp. 317-325
170. F. Schoepfer, A.K. Louis, T. Schuster, Nonlinear iterative methods for linear ill-posed problems in Banach spaces. Inverse Probl. 22, 311-329 (2006)
171. S. Setzer, G. Steidl, Variational methods with higher order derivatives in image processing, in Approximation XII, ed. by M. Neamtu, L.L.Schumaker (Nashboro Press, Brentwood, 2008), pp. 360-386
172. S. Setzer, G. Steidl, T. Teuber, Infimal convolution regularizations with discrete l1-type functionals. Comm. Math. Sci. 9, 797-872 (2011)
173. D.L. Snyder, A.M. Hammoud, R.L.White, Image recovery from data acquired with a chargecoupled-device camera. J. Opt. Soc. Am. A 10, 1014-1023 (1993)
174. D.L. Snyder, C.W. Helstrom, A.D. Lanterman, M. Faisal, R.L. White, Compensation for readout noise in CCD images. J. Opt. Soc. Am. A 12, 272-283 (1995)
175. G. Steidl, A note on the dual treatment of higher order regularization functionals. Computing 76, 135-148 (2006)
176. G. Steidl, S. Didas, J. Neumann, Relations between higher order TV regularization and support vector regression, in Scale-Space and PDE Methods in Computer Vision, ed. by R. Kimmel, N. Sochen, J. Weickert (Springer, Berlin, 2005), pp. 515-527
177. G. Steidl, S. Setzer, B. Popilka, B. Burgeth, Restoration of matrix fields by second order cone programming. Computing 81, 161-178 (2007)
178. D. Strong, T. Chan, Exact Solutions to Total Variation Regularization Problems. CAM-Report 96-46, UCLA, 1996
179. D.M. Strong, J.F. Aujol, T. Chan, Scale recognition, regularization parameter selection, and Meyer's G norm in total variation regularization. SIAM J. Multiscale Model. Simul. 5, 273-303 (2006)
180. R. Stück, M. Burger, T. Hohage, The iteratively regularized GaussUNewton method with convex constraints and applications in 4Pi microscopy. Inverse Probl. 28, 015012 (2012)
181. E. Tadmor, S. Nezzar, L. Vese, A multiscale image representation using hierarchical (BV;L2) decompositions. Multiscale Model. Simul. 2, 554-579 (2004)
182. E. Tadmor, S. Nezzar, L. Vese, Multiscale hierarchical decomposition of images with applications to deblurring, denoising and segmentation. Comm.Math. Sci. 6, 281-307 (2008)
183. Y. Vardi, L.A. Shepp, L. Kaufman, A statistical model for Positron emission tomography. JASA 80, 8-37 (1985)
184. J. Velikina, S. Leng, G.H. Chen, Limited view angle tomographic image reconstruction via total variation minimization. Proc. SPIE v6510 i1
185. L. Vese, L. Lieu, Image restoration and decomposition via bounded total variation and negative Hilbert-Sobolev spaces. Appl. Math. Optim. 58, 167-193 (2008)
186. L. Vese, S. Osher, Modeling textures with total variation minimization and oscillating patterns in image processing. J. Sci. Comput. 19, 533-572 (2003)
187. J. Velikina, S. Leng, G.-H. Chen, Limited view angle tomographic image reconstruction via total variation minimization, in Proceedings of the SPIE 6510, Medical Imaging 2007: Physics of Medical Imaging, 651020, 14 March, 2007. doi:10.1117/12.713750; http://dx.doi. org/10.1117/12.713750
188. K.R. Vixie, Some properties of minimizers for the Chan-Esedoglu L1TV functional. ArXiv 0710.3980 (2007)
189. K.R. Vixie, S.P. Morgan, L1TV computes the flat norm for boundaries. Abstr. Appl. Anal. (2007), Article ID 45153
190. C.R. Vogel, Nonsmooth Regularization, in Inverse Problems in Geophysical Applications, ed. by H.W. Engl et al. (SIAM, Philadelphia, 1997), pp. 1-11
191. C.R. Vogel, Computational Methods for Inverse Problems (SIAM, Philadelphia, 2002)
192. C.R. Vogel,M.E. Oman, Iterative methods for total variation denoising. SIAM J. Sci. Comput. 17, 227-238 (1996)
193. W.W.Wang, P.L. Shui, X.C. Feng, Variational models for fusion and denoising of multifocus images. IEEE Signal Process. Lett. 15, 65-68 (2008)
194. J. Weickert, Anisotropic Diffusion in Image Processing (Teubner, Stuttgart, 1998)
195. J. Weickert, C. Schnörr, A theoretical framework for convex regularizers in PDE-based computation of image motion. Int. J. Comp. Vis. 45, 245-264 (2001)
196. M.Werlberger, T. Pock,M. Unger, H. Bischof, Optical flow guided TV-L1 video interpolation and restoration, in Energy Minimization Methods in Computer Vision and Pattern Recognition, ed. by Y. Boykov, F. Kahl, V. Lempitsky, F.R. Schmidt. Lecture Notes in Computer Science, vol. 6819 (2011), pp. 273-286
197. M.N. Wernick, J.N. Aarsvold (eds.), Emission Tomography: The Fundamentals of PET and SPECT (Academic, San Diego, 2004)
198. D. Wirtz, SEGMEDIX: Development and Application of a Medical Image Segmentation Framework. Diploma thesis, WWU Münster, 2009
199. T. Wittman, Variational Approaches to Digital Image Zooming. PhD thesis, University of Minnesota, 2006
200. J. Xu, S. Osher, Iterative regularization and nonlinear inverse scale space applied to wavelet based denoising. IEEE Trans. Image Proc. 16, 534-544 (2007)
201. Y.F. Yang, T.T. Wu, Z.F. Pang, Image-zooming technique based on Bregmanized nonlocal total variation regularization. Opt. Eng. 50, 097008-097008-10 (2011)
202. Q. Zhang, X. Huang, L. Zhang, An energy-driven total variation model for segmentation and object-based classification of high spatial resolution remote-sensing imagery. IEEE Geosci. Rem. Sens. Lett. 10, 125-129 (2013)
203. X. Zhang,M. Burger, S. Osher, A unified primal-dual algorithm framework based on Bregman iteration. J. Sci. Comp. 3 (2010). doi: 10.1007/s10915-010- 9408-8
204. X. Zhang, M. Burger, X. Bresson, S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. SIAM J. Imag. Sci. 3, 253-276 (2010)
205. M. Zhu, S.J. Wright, T.F. Chan, Duality-based algorithms for total variation image restoration. Comp. Optim. Appl. 47, 377-400 (2010)