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arXiv · 1909.00495

Fourier analysis of periodic Radon transforms

Jesse Railo
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Abstract

We study reconstruction of an unknown function from its $d$-plane Radon transform on the flat $n$-torus when $1 \leq d \leq n-1$. We prove new reconstruction formulas and stability results with respect to weighted Bessel potential norms. We solve the associated Tikhonov minimization problem on $H^s$ Sobolev spaces using the properties of the adjoint and normal operators. One of the inversion formulas implies that a compactly supported distribution on the plane with zero average is a weighted sum of its X-ray data.

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Jesse Railo. 2019-09-02. Fourier analysis of periodic Radon transforms. https://doi.org/10.1007/s00041-020-09775-1

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