In this talk we will discuss my favorite area of research in applied mathematics — the solution of what we call an inverse problem. Never heard of this? That has got to be changed! We will start by discussing the notion of forward and inverse problem based on illustrative, classical examples in imaging sciences, with a focus on medical image computing. We will identify key challenges and talk about ways to alleviate them. We will also introduce some very basic concepts of how to solve these problems on a computer. We will conclude this talk with the conceptual idea of how to efficiently solve inverse problems with a large number of unknowns by using computations carried out simultaneously on more than one computer (parallel computing) by example of CLAIRE, a parallel algorithm for image registration — a classical inverse problem in medical image computing. This solver has been designed to deliver an optimal performance when unleashing the compute power of thousands of computers on the problem. We will show that our implementation (i) allows us to solve problems of unprecedented scale (hundreds of billions of unknowns) in about four minutes and (ii) that we can achieve runtimes of less than two seconds for clinically relevant problem sizes. This talk will be self-contained. No prior knowledge about anything mentioned will be assumed.

Pizza will be served.

deconvolution problem

CLAIRE results