A Wiener Filtering Approach over the Euclidean Motion Group for Radon Transform Inversion

Abstract

The problem of Radon transform inversion arises in fields as diverse as medical imaging, synthetic aperture radar, and radio astronomy. In this paper, we model the Radon transform as a convolution integral over the Euclidean motion group and provide a novel deconvolution method for its inversion. The deconvolution method presented here is a special case of the Wiener filtering framework in abstract harmonic analysis that was recently developed by the author. The proposed deconvolution method provides a fundamentally new statistical formulation for the inversion of the Radon transform that can operate in nonstationary noise and signal fields. It can be utilized for radiation treatment planning, inverse source problems, and 3D and 4D computed tomography. Furthermore, it is directly applicable to many computer vision and pattern recognition problems, as well as to problems in robotics and polymer science. Here, we present an algorithm for the discrete implementation of the Wiener filter and provide a comparison of the proposed image reconstruction method with the filtered back projection algorithms.