Total variation regularization of matrix-valued images

International Journal of Biomedical Imaging

Volumn 2007, Issue , 2007, Pages

  Christiansen, Oddvar ^a   Lee, Tin Man ^b   Lie, Johan ^a   Sinha, Usha ^b   Chan, Tony F ^c  

^a UNIVERSITY OF BERGEN   (Norway)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA REDUCTION; NUMERICAL ANALYSIS; TENSORS;

DIFFUSION MATRIX; DIFFUSION TENSOR IMAGES (DTIS); VARIATION REGULARIZATION; VARIATION RESTORATION;

IMAGING TECHNIQUES;

EID: 34250858225     PISSN: 16874188     EISSN: 16874196     Source Type: Journal    
DOI: 10.1155/2007/27432     Document Type: Article

References (30)

1. P. Perona J. Malik Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12 7 1990 629 639
2. L. I. Rudin S. Osher E. Fatemi Nonlinear total variation based noise removal algorithms. Physica D 60 1992 1-4 259 268
3. M. Lysaker mariul@simula.no S. Osher sjo@math.ucla.edu X.-C. Tai tai@mi.uib.no Noise removal using smoothed normals and surface fitting. IEEE Transactions on Image Processing 13 10 2004 1345 1357
4. T. F. Chan TonyC@college.ucla.edu S. Esedoglu esedoglu@math.ucla.edu Aspects of total variation regularized L1 function approximation. SIAM Journal on Applied Mathematics 65 5 2005 1817 1837
5. T. F. Chan J. Shen Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM Philadelphia, Pa, USA 2005
6. J. Weickert A review of nonlinear diffusion filtering. Proceedings of the 1st International Conference on Scale-Space Theory in Computer Vision Lecture Notes in Computer Science Utrecht, The Netherlands 1252 1997 3 28
7. J. Weickert T. Brox Diffusion and regularization of vector- and matrix-valued images. Fachrichtung 6.1 Mathematik, Universitat des Saarlandes Saarbrücken, Germany preprint no. 58 2002
8. P. J. Basser J. Mattiello D. LeBihan MR diffusion tensor spectroscopy and imaging. Biophysical Journal 66 1 1994 259 267
9. D. Le Bihan J.-F. Mangin C. Poupon Diffusion tensor imaging: concepts and applications. Journal of Magnetic Resonance Imaging 13 4 2001 534 546
10. C.-F. Westin westin@bwh.harvard.edu S. E. Maier H. Mamata A. Nabavi F. A. Jolesz R. Kikinis Processing and visualization for diffusion tensor MRI. Medical Image Analysis 6 2 2002 93 108
11. S. Mori susumu@mri.jhu.edu P. B. Barker Diffusion magnetic resonance imaging: its principle and applications. The Anatomical Record 257 3 1999 102 109
12. S. Mori susumu@mri.jhu.edu P. C. M. van Zijl Fiber tracking: principles and strategies - a technical review. NMR in Biomedicine 15 7-8 2002 468 480
13. R. Bammer roland@s-word.stanford.edu Basic principles of diffusion-weighted imaging. European Journal of Radiology 45 3 2003 169 184
14. E. O. Stejskal J. E. Tanner Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. The Journal of Chemical Physics 42 1965 1 288 292
15. E. O. Stejskal Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow. The Journal of Chemical Physics 43 1965 10 3597 3603
16. P. Tofts Quantitative MRI of the Brain. John Wiley & Sons New York, NY, USA 2005
17. C.-F. Westin westin@bwh.harvard.edu S. E. Maier H. Mamata A. Nabavi F. A. Jolesz R. Kikinis Processing and visualization for diffusion tensor MRI. Medical Image Analysis 6 2 2002 93 108
18. Z. Wang B. C. Vemuri vemuri@cise.ufl.edu Y. Chen T. H. Mareci A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI. IEEE Transactions on Medical Imaging 23 8 2004 930 939
19. D. Tschumperlé R. Deriche Variational frameworks for DT-MRI estimation, regularization and visualization. Proceedings of the 9th IEEE International Conference on Computer Vision (ICCV '03) Nice, France 1 2003 116 121
20. C.-F. Westin H. Knutsson R. Moreno-Diaz F. Pichler Tensor field regularization using normalized convolution. Proceedings of the 9th International Conference on Computer Aided Systems Theory (EUROCAST '03) Lecture Notes in Computer Science 2809 Las Palmas de Gran Canaria, Canary Islands, Spain 2003 564 572
21. B. Chen E. W. Hsu edward.hsu@duke.edu Noise removal in magnetic resonance diffusion tensor imaging. Magnetic Resonance in Medicine 54 2 2005 393 401
22. C. Chefd'hotel christophe.chefdhotel@scr.siemens.com D. Tschumperlé David.Tschumperle@sophia.inria.fr R. Deriche Rachid.Deriche@sophia.inria.fr O. Faugeras Olivier.Faugeras@sophia.inria.fr Regularizing flows for constrained matrix-valued images. Journal of Mathematical Imaging and Vision 20 1-2 2004 147 162
23. Y. Gur yanivg@post.tau.ac.il N. Sochen sochen@post.tau.ac.il Denoising tensors via Lie group flows. Proceedings of the 3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision (VLSM '05) Springer Beijing, China Lecture Notes in Computer Science 3752 2005 13 24
24. D. Groisser groisser@math.ufl.edu Some differential-geometric remarks on a method for minimizing constrained functionals of matrix-valued functions. Journal of Mathematical Imaging and Vision 24 3 2006 349 358
25. P. Blomgren blomgren@math.ucla.edu T. F. Chan chan@math.ucla.edu Color TV: total variation methods for restoration of vector-valued images. IEEE Transactions on Image Processing 7 3 1998 304 309
26. T. F. Chan chan@math.ucla.edu G. H. Golub golub@sccm.stanford.edu P. Mulet mulet@uv.es A nonlinear primal-dual method for total variation-based image restoration. SIAM Journal of Scientific Computing 20 6 1999 1964 1977
27. G. Sapiro Color snakes. Hewlett Packard Computer Peripherals Laboratory Palo Alto, Calif, USA HPL-95-113 1995
28. The Mathworks MatLab, The Language of Technical Computing. http://www.mathworks.com/matlab/
29. S. Pajevic C. Pierpaoli carlo@helix.nih.gov Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain. Magnetic Resonance in Medicine 42 3 1999 526 540
30. Mori and coworkers, "DTI-studio", http://cmrm.med.jhmi.edu/