  The paper addresses the generalization of the half-quadratic minimization
method for the restoration of images having values in a complete Riemannian
manifold. We recall the half-quadratic minimization method using the notation
of the c-transform and adapt the algorithm to our special variational setting.
We prove the convergence of the method for Hadamard spaces. Extensive numerical
examples for images with values on spheres, in the rotation group SO(3) and in
the manifold of positive definite matrices demonstrate the excellent
performance of the algorithm. In particular, the method with SO(3)-valued data
shows promising results for the restoration of images obtained from Electron
Backscattered Diffraction which are of interest in material science.
