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A number of practically important imaging problems involve inverting thegeneralized Radon transform (GRT) $\mathcal R$ of a function $f$ in $\mathbbR^3$. On the other hand, not much is known about the spatial resolution of thereconstruction from discretized data. In this paper we study how accurately andwith what resolution the singularities of $f$ are reconstructed. The GRTintegrates over a fairly general family of surfaces $\mathcal S_y$ in $\mathbbR^3$. Here $y$ is the parameter in the data space, which runs over an open set$\mathcal V\subset\mathbb R^3$. Assume that the data $g(y)=(\mathcal R f)(y)$are known on a regular grid $y_j$ with step-sizes $O(\epsilon)$ along eachaxis, and suppose $\mathcal S=\text{singsupp}(f)$ is a piecewise smoothsurface. Let $f_\epsilon$ denote the result of reconstruction from the descretedata. We obtain explicitly the leading singular behavior of $f_\epsilon$ in an$O(\epsilon)$-neighborhood of a generic point $x_0\in\mathcal S$, where $f$ hasa jump discontinuity. We also prove that under some generic conditions on$\mathcal S$ (which include, e.g. a restriction on the order of tangency of$\mathcal S_y$ and $\mathcal S$), the singularities of $f$ do not lead tonon-local artifacts. For both computations, a connection with the uniformdistribution theory turns out to be important. Finally, we present a numericalexperiment, which demonstrates a good match between the theoretically predictedbehavior and actual reconstruction.

Resolution analysis of inverting the generalized Radon transform from discrete data in $\mathbb R^3$