Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach

Maximilian Baust, Andreas Weinmann, Matthias Wieczorek, Tobias Lasser, Martin Storath, Nassir Navab

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward-backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

Original languageEnglish
Article number7460232
Pages (from-to)1972-1989
Number of pages18
JournalIEEE Transactions on Medical Imaging
Volume35
Issue number8
DOIs
StatePublished - Aug 2016

Keywords

  • Combined denoising and diffusion tensor fitting
  • Total variation minimization
  • diffusion tensor imaging
  • generalized forward-backward algorithm
  • manifold-valued data

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