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Diffusion tensor imaging with deterministic error bounds

Published version
Peer-reviewed

Repository DOI


Type

Article

Change log

Authors

Gorokh, Artur 
Valkonen, Tuomo 

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 (DTI), where correct noise modelling is challenging: it involves the Rician distribution and the nonlinear 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.

Description

Keywords

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

Journal Title

Journal of Mathematical Imaging and Vision

Conference Name

Journal ISSN

0924-9907
1573-7683

Volume Title

56

Publisher

Springer
Sponsorship
Engineering and Physical Sciences Research Council (EP/J009539/1)
Engineering and Physical Sciences Research Council (EP/M00483X/1)
While at the Center for Mathematical Modelling of the Escuela Politécnica Nacional in Quito, Ecuador, T. Valkonen has been supported by a Prometeo scholarship of the Senescyt (Ecuadorian Ministry of Science, Technology, Education, and Innovation). In Cambridge, T. Valkonen has been supported by the EPSRC grants Nr. EP/J009539/1 “Sparse & Higher-order Image Restoration”, and Nr. EP/M00483X/1 “Efficient computational tools for inverse imaging problems”. A. Gorokh and Y. Korolev are grateful to the RFBR (Russian Foundation for Basic Research) for partial financial support (projects 14-01-31173 and 14-01-91151).