We study the accuracy of reconstruction of a family of functions \(f_\epsilon (x)\) , \(x\in \mathbb R^2\) , \(\epsilon \rightarrow 0\) , 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 \(H_0\) , which describes the perturbation, is assumed to have bounded variation. Let \(f_\epsilon ^{\text {rec}}\) denote the reconstruction 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 \(x_0\in \mathcal S\) and \(K_\epsilon \) is an easily computable kernel.
