Let $f$ be an unknown function in $\mathbb R^2$, and $f_\epsilon$ be its reconstruction from discrete Radon transform data, where $\epsilon$ is the data sampling rate. We study the resolution of reconstruction when $f$ has a jump discontinuity along a nonsmooth curve $\mathcal S_\epsilon$. The assumptions are that (a) $\mathcal S_\epsilon$ is an $O(\epsilon)$-size perturbation of a smooth curve $\mathcal S$, and (b) $\mathcal S_\epsilon$ is Holder continuous with some exponent $\gamma\in(0,1]$. We compute the Discrete Transition Behavior (or, DTB) defined as the limit $\text{DTB}(\check x):=\lim_{\epsilon\to0}f_\epsilon(x_0+\epsilon\check x)$, where $x_0$ is generic. We illustrate the DTB by two sets of numerical experiments. In the first set, the perturbation is a smooth, rapidly oscillating sinusoid, and in the second - a fractal curve. The experiments reveal that the match between the DTB and reconstruction is worse as $\mathcal S_\epsilon$ gets more rough. This is in agreement with the proof of the DTB, which suggests that the rate of convergence to the limit is $O(\epsilon^{\gamma/2})$. We then propose a new DTB, which exhibits an excellent agreement with reconstructions. Investigation of this phenomenon requires computing the rate of convergence for the new DTB. This, in turn, requires completely new approaches. We obtain a partial result along these lines and formulate a conjecture that the rate of convergence of the new DTB is $O(\epsilon^{1/2}\ln(1/\epsilon))$.

翻译：美元是一个未知的函数, 在 $\ mathbb R% 2 美元中, 美元是一个未知的函数, 美元是它从离散的 Radon 转换数据中重建的 $\ epsilon 。 当$$是数据取样率时, 我们研究重建的解决方案。 当美元在非悬浮的曲线中出现跳跃不连续时 $\ mathcal Söpsilon $ 。 假设是 (a) $\ mathcal S ⁇ #luslon$ (\ epsilon) 是一个粗略的螺旋 $ (x_ 0\ epslon\ check x$ 美元 美元), (b) $\ massaldal 转换数据转换数据转换为$\ gammam\ 美元( 0, 1美元) 。 我们理解dcread decread deal deal dislation ral disal ration 。