18th GAMM-Seminar Leipzig on
Multigrid and related methods for optimization problems

Max-Planck-Institute for Mathematics in the Sciences
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  18th GAMM-Seminar
January, 24th-26th, 2002
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  Abstract Stefan Henn, Thu, 16.00-16.25 Previous Contents Next  
  Nonlinear Tikhonov Regularization For Digital Image Registration
Stefan Henn (Heinrich-Heine Universität Düsseldorf)

We consider an inverse problem for digital image registration with application to medical imaging. In image registration, we are interested in estimating a vector of displacements tex2html_wrap_inline7 (whose components are functions of the variables tex2html_wrap_inline5). Thus, we search a deformation


that transforms one image called the template T into another similar image, R called the reference, so that


This yields a nonlinear ill conditioned inverse problem. Due to the noise sensitivity of the inverse problem, a Tikhonov regularization method that incorporates additional information is applied in order to rule out discontinuous and irregular solutions to the minimization problem. An important issue is a proper choice of the regularization parameter. For the practical choice of the parameter we use iterative regularization methods. Nonlinear multigrid techniques are used to solve the resulting Euler-Lagrange equations. To obtain a suitable initial guess, we use an approach similar to the full multigrid approach.

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