Gabor frames on the sphere and reconstruction of crystallographic structures
University of Aveiro, Portugal
One major problem in computational mathematics is the reconstruction of cristallographic structures 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 since the data alone are already given over the product of two spheres (one for the incidence ray and the other for the defracted ray). In this talk we will give a short introduction into the problem and the spherical X-ray transform. Afterwards, we discuss the construction of corresponding Gabor frames and an appropriate numerical method for the inversion of the spherical X-ray transform. Since our reduction of the computational costs will be based on sparsity assumptions we will present an adaptation of the accelerated steepest descent method which promotes sparsity constraints.
ISSN 1611 - 4086 | © IKM 2015