Dr. Andreas Mang, University of Houston

Mar-28-2023, 10:30 am

**Abstract**– In this talk, we will discuss efficient numerical algorithms for the solution of PDE-constrained optimization problems governed by hyperbolic transport equations. We will consider applications in medical imaging, and, in particular, an inverse problem referred to as image registration. Here, we are given two images as inputs and seek a spatial transformation that maps points in one image (the template image) to corresponding points in the other image (the reference image). We limit the space of admissible maps y to the group of diffeomorphisms parameterized by smooth, time-dependent velocity fields v. We will explore different formulations and discuss various strategies for their numerical solution. In particular, we will augment the considered hyperbolic PDE constraint that models the transport of image intensities by adding incompressibility constraints as well as an Euler-Poincaré equation of the diffeomorphism group. Our contributions are in the design of numerical methods and computational kernels that scale on heterogeneous, high-performance computing platforms. Our solvers are based on state-of-the-art algorithms to enable fast convergence and short runtime. We consider adjoint-based methods for optimization that exploit first- and second-order derivative information. We will showcase results for real and synthetic data to analyze rate of convergence, time-to-solution, numerical accuracy, and scalability of our solvers. As a highlight, we will showcase results for a GPU-accelerated implementation termed CLAIRE that allows us to solve clinically relevant 3D image registration problems with high accuracy in under 5 seconds on a single GPU and scales up to 100s of GPUs.