Diffusion Tensor Imaging with Deterministic Error Bounds

Artur Gorokh, Yury Korolev, Tuomo Valkonen

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)

Abstract

Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices. We present some existing results of the theory of regularisation in this novel framework, where errors are represented as bounds by means of the appropriate partial order. We apply the theory to diffusion tensor imaging, where correct noise modelling is challenging: it involves the Rician distribution and the non-linear Stejskal–Tanner equation. Linearisation of the latter in the statistical framework would complicate the noise model even further. We avoid this using the error bounds approach, which preserves simple error structure under monotone transformations.

Original languageEnglish
Pages (from-to)137-157
Number of pages21
JournalJournal of Mathematical Imaging and Vision
Volume56
Issue number1
DOIs
Publication statusPublished - 1 Sep 2016

Keywords

  • Deterministic
  • Diffusion tensor imaging
  • Error bounds
  • Noise modelling
  • Total generalised variation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics

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