Total variation regularization of matrix-valued images

Oddvar Christiansen*, Tin Man Lee, Johan Lie, Usha Sinha, Tony F. Chan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish (US)
Article number27432
JournalInternational Journal of Biomedical Imaging
StatePublished - 2007
Externally publishedYes

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging


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