Justin Buhendwa Nyenyezi (ISP-Bukavu, DRC) – POSTPONED

Title: A Low-rank tensor based preconditioner for accelerating deformable 3D medical image registration

Abstract: Modeled as a variational problem, the deformable 3D image registration problem needs to solve a sequence of linear systems during the optimization process. Although these linear systems are sparse and structured, they are very large and ill conditioned. This leads to low convergence rate of the algorithms used to solve the problem or to inaccurate solutions.

Since it is observed that much of the time is spent in the solution of these linear systems, there is a need to provide efficient system solvers. Let N be the number of voxels in the image. Algorithms with linear complexity O(N ) based on fast Discrete Cosine Transforms or additive spliting operator are yet available. However, this linear complexity may be far too large for large 3D medical images. In our current study, we examine the contribution of a specific Low-rank preconditioner in a tensor-train format. We argue that, this preconditioner offers the most compromise between complexity and precision, since it allows to replace this linear
complexity by a logarithmic complexity O(log N ).

For this purpose, we first propose to use a compressed representation of data with a given accuracy ε using tensor train format. Then, within this tensor train format, we propose this low-rank preconditioner build with spectral information to speedup and stabilize the system solver. A benchmark of some registration algorithms on a large set of 3D medical images and different from their linear system solvers is provided. The benchmark relies on the perfomance profile based on the earlier decrease of the function value.