7 papers
Discrete to continuum limits in Bayesian inverse problems
Alexander Katsevich
We develop a posterior-level discrete-to-continuum theory for Bayesian inverse problems whose finite-dimensional priors arise from local finite-difference regularization and whose…
High-dimensional Laplace asymptotics up to the concentration threshold
Alexander Katsevich, Anya Katsevich
We study high-dimensional Laplace-type integrals in the regime where both and are large. Existing rigorous Laplace-e…
Local Characterization of Noise in Iterative Reconstruction of the Generalized Radon Transform
Alexander Katsevich
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 fra…
Local analysis of iterative reconstruction from discrete generalized Radon transform data in the plane
Alexander Katsevich
Local reconstruction analysis (LRA) is a powerful and flexible technique to study images reconstructed from discrete generalized Radon transform (GRT) data, . The m…
Analysis of reconstruction from noisy discrete generalized Radon data
Alexander Katsevich
We consider a wide class of generalized Radon transforms , which act in for any and integrate over submanifolds of any codimension , $1\le N\…
Local reconstruction analysis of inverting the Radon transform in the plane from noisy discrete data
Anuj Abhishek, Alexander Katsevich, James W. Webber
In this paper, we investigate the reconstruction error, $N_\e^{\text{rec}}(x)$, when a linear, filtered back-projection (FBP) algorithm is applied to noisy, discrete Radon transfor…
Analysis of reconstruction of functions with rough edges from discrete Radon data in
Alexander Katsevich
We study the accuracy of reconstruction of a family of functions , , , from their discrete Radon transform data sampled with step size . For e…