Many interesting image processing problems can be solved by finding suitable minimizers of a variational model. In this talk, we consider models where the unknowns reside in a space of measures. We will consider theoretical results and discuss some applications, in particular in diffusion-weighted imaging, manifold-valued optimization and approximation of non-convex problems.
joint work with Angelica Aviles-Rivero, Veronica Corona, Carole Le Guyader, Carola-Bibiane Schönlieb, Martin Graves, Guy Williams
This work addresses a central topic in Magnetic Resonance Imaging (MRI) which is the motion-correction problem in a joint reconstruction and registration framework. From a set of multiple MR acquisitions corrupted by motion, we aim at jointly reconstructing a single high quality motion-free corrected image and retrieving the physiological dynamics through the deformation maps. To this purpose, we propose a novel variational model relying on hyperelasticity and compressed sensing principles.
joint work with Fjedor Gaede, Martin Burger
In this talk we present an efficient coarse-to-fine optimization strategy for sparsification of large point clouds modeled via finite weighted graphs. Our method is derived from the recently proposed Cut Pursuit strategy and leads to a significant speed up (up to factor 120) in computing optimizers for a family of related variational problems. We demonstrate results on both unperturbed as well as noisy 3D point cloud data.