Restoration of Manifold-Valued Images by Half-Quadratic Minimization
It provides a theoretically grounded restoration method for manifold-valued images, benefiting material science applications like EBSD image restoration.
The paper extends half-quadratic minimization to restore manifold-valued images, proving convergence for Hadamard spaces and demonstrating excellent performance on spheres, SO(3), and positive definite matrices.
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.