Radon transform inversion via Wiener filtering over the Euclidean motion group

In this paper we formulate the Radon transform as a convolution integral over the Euclidean motion group (SE(2)) and provide a minimum mean square error (MMSE) stochastic deconvolution method for the Radon transform inversion. Proposed approach provides a fundamentally new formulation that can model nonstationary signal and noise fields. Key components of our development are the Fourier transform over SE(2), stochastic processes indexed by groups and fast implementation of the SE(2) Fourier transform. Numerical studies presented here demonstrate that the method yields image quality that is comparable or better than the filtered backprojection algorithm. Apart from X-ray tomographic image reconstruction, the proposed deconvolution method is directly applicable to inverse radiotherapy, and broad range of science and engineering problems in computer vision, pattern recognition, robotics as well as protein science.