Algorithmic Aspects of Tomographic Reconstruction from Parallel and Diffracted Projections
Michael Liebling, EPFL LIB

Test Run • 13 February 2003

Abstract
We review our recent work on a high-quality discretization of the Radon transform and filtered back-projection. We focus on issues regarding the trade-off between interpolation model, sampling-step size, number of projections, and computational complexity. We then present a wavelet-based approach for the reconstruction of images from different kinds of measurements: digital holograms, and projections obtained by optical diffraction tomography. It is based on Fresnelet bases, which are wavelets that we have specifically designed for problems involving wave propagation. Numerical experiments on synthetic and real-world data demonstrate the soundness of our approach.