The Radon transform on SO(3): a Fourier slice theorem and numerical inversion

R Hielscher, D Potts, J Prestin, H Schaeben, M Schmalz
2008 Inverse Problems  
The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill posed inverse problem which applies to X-ray tomography with polycrystalline materials. This communication presents a novel approach to the numerical inversion of the one-dimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete inverse Radon transform of a function sampled on the product space S 2 × S 2 of two two-dimensional spheres is determined as the solution of a
more » ... n problem, which is iteratively solved using fast Fourier techniques for S 2 and SO(3). The favorable complexity and stability of the algorithm based on these techniques has been confirmed with numerical tests.
doi:10.1088/0266-5611/24/2/025011 fatcat:3oq2efczhvgvpjctiakr3acjia