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In this paper we study reconstruction of a function $f$ from its discreteRadon transform data in $\mathbb R^3$ when $f$ has jump discontinuities.Consider a conventional parametrization of the Radon data in terms of theaffine and angular variables. The step-size along the affine variable is$\epsilon$, and the density of measured directions on the unit sphere is$O(\epsilon^2)$. Let $f_\epsilon$ denote the result of reconstruction from thediscrete data. Pick any generic point $x_0$ (i.e., satisfying some mildconditions), where $f$ has a jump. Our first result is an explicit leading termbehavior of $f_{\epsilon}$ in an $O(\epsilon)$-neighborhood of $x_0$ as$\epsilon\to0$.  A closely related question is why can we accurately reconstruct functionswith discontinuities at all? This is a fundamental question, which has not beenstudied in the literature in dimensions three and higher. We prove that thediscrete inversion formula `works', i.e. if $x_0\not\in S:=\text{singsupp}(f)$is generic, then $f_{\epsilon}(x_0)\to f(x_0)$ as $\epsilon\to0$. The proof ofthis result reveals a surprising connection with the theory of uniformdistribution (u.d.). This is a new phenomenon that has not been knownpreviously. We also present some numerical experiments, which confirm thevalidity of the developed theory.

Analysis of reconstruction from discrete Radon transform data in $\mathbb R^3$ when the function has jump discontinuities