Sampling Conditions for the Circular Radon Transform

Recovering a function from circular or spherical mean values is the basis of many modern imaging technologies, such as photo and thermoacoustic computed tomography or ultrasound reflection tomography. Recently, much progress has been made concerning the problem of recovering a function from its circular mean values (its circular Radon transform). In particular, theoretically exact inversion formulas of the back-projection type have been discovered using continuously sampled data. In practical applications, however, only a discrete number of circular mean values can be collected. In this paper, we address this issue in the context of the Shannon sampling theory. We derive sharp sampling conditions for the number of angular and radial samples, such that any essentially b₀-bandlimited function can be recovered from a finite number of such circular mean values.