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

What is it about?

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 paper 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 minimization 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.

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