Analysis of view aliasing for the generalized Radon transform in ℝ^2

02/02/2023

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by   Alexander Katsevich, et al.

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In this paper we consider the generalized Radon transform ℛ in the plane. Let f be a piecewise smooth function, which has a jump across a smooth, convex curve 𝒮. We obtain a precise, quantitative formula describing view aliasing artifacts when f is reconstructed from the data ℛ f discretized in the view direction. The formula is asymptotic, it is established in the limit as the sampling rate ϵ→0. The proposed approach does not require that f be band-limited. Numerical experiments with the classical Radon transform and generalized Radon transform (which integrates over circles) demonstrate the accuracy of the formula.