Moakher, Maher (National Engineering School at Tunis, Univ. of Tunis El-Manar)

A Riemannain Framework for the Averaging, Smoothing and Interpolation of Some Matrix-Valued Data

Scheduled for presentation during the Mini-Symposium "Geometric Optimisation in Systems and Control II" (ThA07), Thursday, July 27, 2006, 11:15−11:40, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

The availability of new technologies in many fields of science has made it possible to acquire and store quite easily a huge amount of data. However, these data are generally corrupted with noise of different sources. It is therefore necessary to remove or reduce the noise before meaningful information could be extracted from them. In many situations, these data are subjected to nonlinear constraints. Symmetric ositive-definite diffusion tensors from Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data, special Euclidean matrices from motion data, rotation matrices from orientation data, and unit vectors from directional data, are but few examples of constrained data. We use a Riemannian framework for the introduction of properly invariant means of element in some Riemannian symmetric spaces. We describe the use of these means for the smoothing of noisy data, and for the interpolation and averaging of discrete data on some smoothly constrained data. Some applications of these procedures for problems in engineering and biology are discussed.