Speaker: Andreas Weinmann (Hochschule Darmstadt and Helmholtz Center Munich)

Title: Variational methods for the restauration of manifold-valued images and data

Abstract: Nonlinear manifolds appear as data spaces in various applications. One example in image processing is diffusion tensor imaging, where the data sitting in every voxel is a positive matrix representing the diffusibility of water molecules measured at the corresponding spatial location. Another example is color image processing, where instead of the RGB representation often other formats such as HSI or HSV are used which employ a circle to represent the hue of a color. A third example are registration problems (e.g., between a camera and an ultrasound devise) where time series of euclidean motions appear. Since the measured data is often noisy, regularization of these nonlinear data is necessary. In this talk, we propose algorithms for the variational regularization of manifold-valued data using non-smooth functionals. In particular, we deal with algorithms for TV regularization and with higher order methods including the TGV denoising of manifold-valued data. We present concrete applications in medical imaging tasks.