A variational model with fractional-order regularization term arising in registration of diffusion tensor image

Huan Han

doi:10.3934/ipi.2018053

Article Contents

2018, Volume 12, Issue 6: 1263-1291. Doi: 10.3934/ipi.2018053

This issue Previous Article Next Article Reconstruction of the coefficients of a star graph from observations of its vertices

A variational model with fractional-order regularization term arising in registration of diffusion tensor image

Huan Han^,

School of Mathematics and Physics, China University of Geosciences, Wuhan 430076, China

* Corresponding author: Huan Han
* Corresponding author: Huan Han

Received: December 1, 2016

Revised: August 1, 2018

Published online: October 11, 2018

The first author is supported by NSFC under grant No.11471331 and partially supported by National Center for Mathematics and Interdisciplinary Sciences.

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Abstract

In this paper, a new variational model with fractional-order regularization term arising in registration of diffusion tensor image(DTI) is presented. Moreover, the existence of its solution is proved to ensure that there is a regular solution for this model. Furthermore, three numerical tests are also performed to show the effectiveness of this model.

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Mathematics Subject Classification: Primary: 68U10, 62H35, 74G65, 94A08, 97M10, 58E05; Secondary: 49J45, 49J35.

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Figure 1. One slice of $T(\cdot)$ and $D(\cdot)$

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Figure 2. $a$ and ${\rm Re-SSD}$ change with differential order $\alpha$

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Figure 3. $a$ and ${\rm Re-SSD}$ change with time $s$ in iteration process

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Figure 4. The 22th slice of $T\diamond h(\cdot)$

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