Restoration of Manifold-Valued Images by Half-Quadratic Minimization

Abstract

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.

References in corpus (2)

• A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images
• A Second Order TV-type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data

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