Local reconstruction analysis of inverting the Radon transform in the plane from noisy discrete data

In this paper, we investigate the reconstruction error, N_^rec (x), when a linear, filtered back-projection (FBP) algorithm is applied to noisy, discrete Radon transform data with sampling step size in two-dimensions. Specifically, we analyze N_^rec (x) for x in small, O () -sized neighborhoods around a generic fixed point, x₀, in the plane, where the measurement noise values, ₊, ₉ (i. e. , the errors in the sinogram space), are random variables. The latter are independent, but not necessarily identically distributed. We show, under suitable assumptions on the first three moments of the ₊, ₉, that the following limit exists: N^rec (;x₀) = ₀N_^rec (x₀+), for x in a bounded domain. Here, N_^rec and N^rec are viewed as continuous random variables, and the limit is understood in the sense of distributions. Once the limit is established, we prove that N^rec is a zero mean Gaussian random field and compute explicitly its covariance. In addition, we validate our theory using numerical simulations and pseudo random noise.