Reconstruction from Radon projections and orthogonal expansion on a ball

Details Reconstruction from Radon projections and orthogonal expansion on a ball Reconstruction from Radon projections and orthogonal expansion on a ball

2007-05-14

arxiv.org/abs/0705.1984v1

Physics

Mathematical Physics

15 pages

Scientific paper

10.1088/1751-8113/40/26/010

The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to algorithms for image reconstruction from Radon data. The relation between orthogonal expansion and the singular value decomposition of the Radon transform is also exploited.

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