Development and Study of Optimization Algorithms for Medical Image Registration Problems

Abstract

In medical image analysis, image registration aims at analyzing several images acquired at different times or by different devices. More precisely, it determines the suitable spatial transformation that allows these images to be aligned in a common spatial domain.
The common issues that are known for the deformable 3D image registration problem include the computing time that, especially for non-parametric transformations, may be quite troublesome for some clinical applications. This thesis is concerned with the analysis of numerical algorithms designed to solve efficiently the medical image registration problem with a focus on the use of preconditioners to speedup iterative linear system solvers. Our purpose is two-fold. First, we propose an extension in the use of an existing package, FAIR from Jan Modersitzki, by allowing the user to choose polynomial preconditioners and/or to choose large deformations. Second, if applicable, we propose to use a compressed representation of data with a given accuracy $\epsilon$ using Tensor-Train format to solve efficiently the linear systems. Within this tensor format, a low-rank preconditioner built with spectral information is used to speedup and stabilize the system solver.

Date of Award	17 May 2018
Original language	English
Awarding Institution	University of Namur
Sponsors	CERUNA
Supervisor	Annick Sartenaer (Supervisor), Anne Lemaitre (President), Daniel RUIZ (Jury), Hubert Meurisse (Jury) & Lieven De Lathauwer (Jury)