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- W2060773902 abstract "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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>D</mml:mi></mml:math>implicitly as the product<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:msup><mml:mi>L</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math>, and work with the elements of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>L</mml:mi></mml:math>as variables, instead of working directly on the elements of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>D</mml:mi></mml:math>. 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." @default.
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- W2060773902 date "2007-01-01" @default.
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- W2060773902 title "Total Variation Regularization of Matrix-Valued Images" @default.
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- W2060773902 doi "https://doi.org/10.1155/2007/27432" @default.
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