The noisy spherical Radon transform and Gabor frames on the sphere
Speaker:Prof. Paula Cerejeiras
Associate Professor
Universidade de Aveiro
Date & Time:12 May 2011 (Thursday) 16:00 - 17:00
Venue:J322
Organized by:Department of Mathematics

Abstract

In this talk we address the problem of numerical reconstruction of crystallographic structures departing from defraction measurements. Since it requires the inversion of the spherical X-ray transform it represents both an ill-posed inverse problem as well as a computationally intensive problem, this last one due to the fact that the data alone are already given in terms of a grid of the product of two spheres (one for the incidence ray and the other for the defracted ray). We will give a short introduction into this problem and the spherical Xray transform. Afterwards, we discuss the construction of corresponding Gabor frames and an appropriate numerical method based on sparsity constrains for the inversion of the spherical X-ray transform.

Biography

Paula Cerejeiras has obtained her PhD degree in Mathematics in 1997. Her main interests are in Clifford analysis, Radon transformations, wavelet analysis and inverse problems. She has more than 40 publications, among them papers in such journals as Applied and Computational Harmonic Analysis and in Communications in Pure and Applied Analysis. Furthermore, she has coordinated and participated in several international projects and is currently associated professor at the Mathematical Department of the University of Aveiro.