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
(whose components are functions of the variables
).
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.