KAUST Research Workshop on Optimization and Big Data
University of Cambridge
Matthias J. Ehrhardt is a post-doctoral research associate in the Cambridge Image Analysis group at the Department for Applied Mathematics and Theoretical Physics, University of Cambridge. Previously he has been with the Centre for Inverse Problems and the Centre for Medical Image Computing at the University College London (UCL). He obtained his PhD from UCL in 2015 and his Diploma from the University of Bremen, Germany in 2012. His research interests comprise inverse problems, non-smooth / (non-)convex / stochastic optimization, sparsity, and signal and image processing in particular application of these techniques to medical imaging.
A very popular algorithm for image processing and image reconstruction with non-differentiable priors is the primal-dual hybrid gradient (PDHG) algorithm proposed by Chambolle and Pock. In some scenarios it is beneficial to employ a stochastic version of this algorithm where not all of the dual updates are executed simultaneously. It turns out that the stochastic version has convergence rates along the same lines as the deterministic PDHG. Numerical results on clinical positron emission tomography (PET) data show a dramatic speed up by the proposed method and thereby the impact this may have on clinical applications. This is joint work with A. Chambolle, P. Markiewicz, P. Richtárik, J. Schott and C. Schoenlieb.