Abstract

Co-authors: Martin Benning (University of Cambridge), Dan Holland (University of Cambridge), Lyn Gladden (University of Cambridge), Carola-Bibiane Schnlieb (University of Cambridge), Florian Knoll (New York University), Kristian Bredies (University of Graz)

Many inverse problems inherently involve non-linear forward operators. In this talk, I concentrate on two examples from magnetic resonance imaging (MRI). One is modelling the Stejskal-Tanner equation in diffusion tensor imaging (DTI), and the other is decomposing a complex image into its phase and amplitude components for MR velocity imaging, in order to regularise them independently. The primal-dual method of Chambolle and Pock being advantageous for convex problems where sparsity in the image domain is modelled by total variation type functionals, I recently extended it to non-linear operators. Besides motivating the algorithm by the above applications, through earlier collaborative efforts using alternative convex models, I will sketch the main ingredients for proving local convergence of the method. Then I will demonstrate very promising numerical performance.