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
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CLAIRE results
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