This title appears in the Scientific Report : 2006 
A multigrid method for anisotropic PDEs in elastic image registration
Hömke, L.
Institut für Medizin; IME
Numerical linear algebra with applications, 13 (2006)
New York, NY [u.a.] Wiley 2006
10.1002/nla.477
Journal Article
Funktion und Dysfunktion des Nervensystems
Numerical Linear Algebra with Applications 13
J
multigrid
image registration
PDE
anisotropic coefficients
Please use the identifier: http://dx.doi.org/10.1002/nla.477 in citations.


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 (c) 2006 John Wiley & Sons, Ltd.