Journal
JOURNAL OF MATHEMATICAL IMAGING AND VISION
Volume 56, Issue 1, Pages 137-157Publisher
SPRINGER
DOI: 10.1007/s10851-016-0639-7
Keywords
Diffusion tensor imaging; Noise modelling; Total generalised variation; Error bounds; Deterministic
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Funding
- Prometeo scholarship of the Senescyt (Ecuadorian Ministry of Science, Technology, Education, and Innovation)
- EPSRC [EP/J009539/1, EP/M00483X/1]
- RFBR (Russian Foundation for Basic Research) [14-01-31173, 14-01-91151]
- Engineering and Physical Sciences Research Council [EP/J009539/1, EP/M00483X/1] Funding Source: researchfish
- EPSRC [EP/M00483X/1, EP/J009539/1] Funding Source: UKRI
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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.
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