# Polynomial versus Matrix-splitting preconditioners for linear systems arising in 3D medical image registration

Justin Buhendwa Nyenyezi (Orateur)

Activité: Types de discours ou de présentationPrésentation orale

## Description

Many methods exist to solve large sparse linear systems. However, a given method may perform well for a particular problem while it may not work as well for another.
For designing efficient system solvers, one may analyze structures of general operators or matrices used by the algorithms. In non-rigid medical image registration, matrices are derived from physical principles, modelled as Partial Differential Equations (PDEs).
Although these systems are often sparse and structured, they are very large and ill-conditioned. Thus, their solvers are time consuming and their complexity in operation counts is polynomial. As a consequence, fast and superfast direct methods reveal numerical instabilities and thus lead to breakdowns or inaccurate solutions.
In this study, we are especially interested in benchmarking iterative system solvers on a large set of 3D medical images. These system solvers are based on the Conjugate Gradient method but different from the preconditioning techniques .
The ongoing results confirm that there is no single system solver that is the best for all the problems. However, the results indicate which solver has the highest probability of being the best within a factor $f \in [1,\infty[$ and considering a limited computional budget in terms of time and storage requirements.
Période 25 janv. 2018 Namur Institute for Complex Systems