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

2025/09/22 by Alexander Katsevich, Katsevich, Alexander
Computer Science · Medicine · #44A12 #60G60 #65R32 #FOS: Mathematics #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2509.17944

openalex publication_date 2025/09/22 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

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 establish that the rescaled 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. 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: the discreteness of the data and the presence of noise.

Citations

• Statistical microlocal analysis in two-dimensional X-ray CT
• Local analysis of iterative reconstruction from discrete generalized Radon transform data in the plane
• Analysis of reconstruction from noisy discrete generalized Radon data
• Local reconstruction analysis of inverting the Radon transform in the plane from noisy discrete data
• Analysis of reconstruction of functions with rough edges from discrete Radon data in \mathbb R²
• Resolution analysis of inverting the generalized N-dimensional Radon transform in \mathbb Rⁿ from discrete data
• Sampling linear inverse problems with noise
• Efficient Nonparametric Bayesian Inference For X-Ray Transforms
• Cubic convolution interpolation for digital image processing

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