A multigrid method for anisotropic PDEs in elastic image registration

This paper deals with the solution of a non‐linear ill‐conditioned inverse problem arising in digital image registration. In the first part of the paper, we define the problem as the minimization of a regularized non‐linear least‐squares functional, which measures the image difference and smoothness...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2006-03, Vol.13 (2-3), p.215-229
Main Author: Homke, Lars
Format: Article
Language:English
Subjects:
anisotropic coefficients
image registration
multigrid
PDE
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Summary:This paper deals with the solution of a non‐linear ill‐conditioned inverse problem arising in digital image registration. In the first part of the paper, we define the problem as the minimization of a regularized non‐linear least‐squares functional, which measures the image difference and smoothness of the transformation. We study inexact Newton methods for solving this problem, i.e. we linearize the functional around a current approximation and replace the Hessian by a suitable operator in order to obtain well‐posed subproblems in each step of the iteration. These anisotropic subproblems are solved using a multigrid solver. Due to the anisotropy in the coefficients of the underlying equations, standard multigrid solvers suffer from poor convergence rates. We discuss modifications to the multigrid components, specifically to the smoothing procedure, the interpolation and the coarse grid correction. Numerical results that demonstrate the improvements obtained with these new components are given. Copyright © 2006 John Wiley & Sons, Ltd.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.477