Total Variation Regularization of Matrix-Valued Images
We generalize the total variation restoration model, introduced by Rudin, Osher, and Fatemi in 1992, to matrix-valued data, in particular, to diffusion tensor images (DTIs). Our model is a natural extension of the color total variation model proposed by Blomgren and Chan in 1998. We treat the diffus...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Biomedical Imaging |
| Online Access: | http://dx.doi.org/10.1155/2007/27432 |
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| _version_ | 1832551890441732096 |
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| author | Oddvar Christiansen Tin-Man Lee Johan Lie Usha Sinha Tony F. Chan |
| author_facet | Oddvar Christiansen Tin-Man Lee Johan Lie Usha Sinha Tony F. Chan |
| author_sort | Oddvar Christiansen |
| collection | DOAJ |
| description | We generalize the total variation restoration model, introduced by Rudin, Osher, and Fatemi in 1992, to matrix-valued data, in particular, to diffusion tensor images (DTIs). Our model is a natural extension of the color total variation model proposed by
Blomgren and Chan in 1998. We treat the diffusion matrix D implicitly as the product D=LLT, and work with the elements of L as variables, instead of working directly on the elements of D. This ensures positive definiteness of the tensor during the regularization flow, which is essential when regularizing DTI. We perform numerical experiments on both synthetical data and 3D human brain DTI, and measure the quantitative behavior of the proposed model. |
| format | Article |
| id | doaj-art-8bf7ec7b1b8041ac826144f1cc73cb5f |
| institution | Kabale University |
| issn | 1687-4188 1687-4196 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Biomedical Imaging |
| spelling | doaj-art-8bf7ec7b1b8041ac826144f1cc73cb5f2025-02-03T06:00:18ZengWileyInternational Journal of Biomedical Imaging1687-41881687-41962007-01-01200710.1155/2007/2743227432Total Variation Regularization of Matrix-Valued ImagesOddvar Christiansen0Tin-Man Lee1Johan Lie2Usha Sinha3Tony F. Chan4Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Bergen, Bergen 5008, NorwayMedical Imaging Informatics Group, Department of Radiological Sciences, University of California, Los Angeles, 90024, CA, USADepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Bergen, Bergen 5008, NorwayMedical Imaging Informatics Group, Department of Radiological Sciences, University of California, Los Angeles, 90024, CA, USADivision of Physical Sciences, College of letters science, University of California, Los Angeles, 90095, CA, USAWe generalize the total variation restoration model, introduced by Rudin, Osher, and Fatemi in 1992, to matrix-valued data, in particular, to diffusion tensor images (DTIs). Our model is a natural extension of the color total variation model proposed by Blomgren and Chan in 1998. We treat the diffusion matrix D implicitly as the product D=LLT, and work with the elements of L as variables, instead of working directly on the elements of D. This ensures positive definiteness of the tensor during the regularization flow, which is essential when regularizing DTI. We perform numerical experiments on both synthetical data and 3D human brain DTI, and measure the quantitative behavior of the proposed model.http://dx.doi.org/10.1155/2007/27432 |
| spellingShingle | Oddvar Christiansen Tin-Man Lee Johan Lie Usha Sinha Tony F. Chan Total Variation Regularization of Matrix-Valued Images International Journal of Biomedical Imaging |
| title | Total Variation Regularization of Matrix-Valued Images |
| title_full | Total Variation Regularization of Matrix-Valued Images |
| title_fullStr | Total Variation Regularization of Matrix-Valued Images |
| title_full_unstemmed | Total Variation Regularization of Matrix-Valued Images |
| title_short | Total Variation Regularization of Matrix-Valued Images |
| title_sort | total variation regularization of matrix valued images |
| url | http://dx.doi.org/10.1155/2007/27432 |
| work_keys_str_mv | AT oddvarchristiansen totalvariationregularizationofmatrixvaluedimages AT tinmanlee totalvariationregularizationofmatrixvaluedimages AT johanlie totalvariationregularizationofmatrixvaluedimages AT ushasinha totalvariationregularizationofmatrixvaluedimages AT tonyfchan totalvariationregularizationofmatrixvaluedimages |