Analysis of reconstruction of functions with rough edges from discrete Radon data in $\mathbb R^2$

We study the accuracy of reconstruction of a family of functions $f\epsilon(x)$, $x\in\mathbb R^2$, $\epsilon\to0$, from their discrete Radon transform data sampled with step size $O(\epsilon)$. For each $\epsilon>0$ sufficiently small, the function $f\epsilon$ has a jump across a rough boundary $\mathcal S\epsilon$, which is modeled by an $O(\epsilon)$-size perturbation of a smooth boundary $\mathcal S$. The function $H0$, which describes the perturbation, is assumed to be of bounded variation. Let $f\epsilon^{{\text{rec}}$} denote the reconstruction, which is computed by interpolating discrete data and substituting it into a continuous inversion formula. We prove that $(f\epsilon^{{\text{rec}}-K\epsilon*f\epsilon)(x_0+\epsilon\check} x)=O(\epsilon^{{1/2}\ln(1/\epsilon))$,} where $x0\in\mathcal S$ and $K\epsilon$ is an easily computable kernel.