Abstract
We study reconstruction of an unknown function from its d-plane Radon transform on the flat torus {mathbb {T}}^n = {mathbb {R}}^n /{mathbb {Z}}^n when 1 le d le 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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