Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles

The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill-posed inverse problem that can be applied to X-ray tomography with polycrystalline materials. This paper is concerned with the development of a method to stably approximate the inverse of the noisy Radon transform on SO(3). The proposed approach is composed by basic building blocks of the coorbit theory on homogeneous spaces, Gabor frame constructions and variational principles for sparse recovery. The performance of the finally obtained iterative approximation is studied through several experiments.