Preconditioning linear systems from deformable 3D medical image registration using tensor train format

Description

Modeled as a variational problem, the medical image registration problem needs to solve a sequence of linear systems during the optimization process. Much of the time is spent in the solution of these linear systems. Indeed, although these systems are sparse and structured, they are very large and ill conditioned.

Algorithms with linear complexity based on fast Discrete Cosine Transforms or additive spliting operator are yet available.
However, this linear complexity is far too large for large 3D medical images.
Our aim is to replace this linear complexity by a logarithmic complexity.
Our proposition is two-fold:
First, we propose to use a compressed representation of data with a given accuracy using tensor train format.
Second, within this tensor train format, we propose a low-rank preconditioner built with spectral informations to speedup and stabilize the system solver.

Period	25 Sept 2017 → 28 Sept 2017
Held at	University of Paderborn, Germany
Degree of Recognition	International