Local Characterization of Noise in Iterative Reconstruction of the Generalized Radon Transform

Abstract.

We study noise in iterative reconstruction from discrete, noisy data of a generalized Radon transform in the plane. Our approach builds on Local Reconstruction Analysis (LRA), a framework for analyzing reconstructions at the native scale. We show that the reconstruction error converges in distribution to a zero-mean Gaussian random field with explicitly computable covariance, providing a complete local characterization of noise in iterative reconstruction. Numerical experiments show strong agreement with the theoretical predictions. Our results advance the theoretical understanding of errors in iterative methods while also offering practical value: reliable predictions of reconstruction error without repeated, costly simulations. Combined with earlier deterministic results, our findings complete the analysis of iterative reconstruction at the native scale with respect to the two most fundamental limitations: data discreteness and measurement noise.