Total generalized variation in diffusion tensor imaging

Valkonen T, Bredies K, Knoll F (2013)

Publication Type: Journal article

Publication year: 2013

Journal

Siam Journal on Imaging Sciences Society for Industrial and Applied Mathematics

Book Volume: 6

Pages Range: 487-525

Journal Issue: 1

DOI: 10.1137/120867172

Abstract

We study the extension of total variation (TV), total deformation (TD), and (second-order) total generalized variation (TGV2) to symmetric tensor fields. We show that for a suitable choice of finite-dimensional norm, these variational seminorms are rotation-invariant in a sense natural and well suited for application to diffusion tensor imaging (DTI). Combined with a positive definiteness constraint, we employ these novel seminorms as regularizers in Rudin-Osher-Fatemi (ROF) type denoising of medical in vivo brain images. For the numerical realization, we employ the Chambolle-Pock algorithm, for which we develop a novel duality-based stopping criterion which guarantees error bounds with respect to the functional values. Our findings indicate that TD and TGV2, both of which employ the symmetrized differential, provide improved results compared to other evaluated approaches. © 2013 Society for Industrial and Applied Mathematics.

Authors with CRIS profile

Florian Knoll

Involved external institutions

Karl-Franzens-Universität Graz AT Austria (AT) Technische Universität Graz AT Austria (AT)

How to cite

APA:

Valkonen, T., Bredies, K., & Knoll, F. (2013). Total generalized variation in diffusion tensor imaging. Siam Journal on Imaging Sciences, 6(1), 487-525. https://doi.org/10.1137/120867172

MLA:

Valkonen, Tuomo, Kristian Bredies, and Florian Knoll. "Total generalized variation in diffusion tensor imaging." Siam Journal on Imaging Sciences 6.1 (2013): 487-525.

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