9 citations · 38 across the 18 of their papers we have counts for
20 papers
Analysis of view aliasing for the generalized Radon transform in
Alexander Katsevich
In this paper we consider the generalized Radon transform in the plane. Let be a piecewise smooth function, which has a jump across a smooth curve . We…
Novel resolution analysis for the Radon transform in for functions with rough edges
Alexander Katsevich
Let be a function in , which has a jump across a smooth curve with nonzero curvature. We consider a family of functions with jumps across a fami…
Resolution of 2D reconstruction of functions with nonsmooth edges from discrete Radon transform data
Alexander Katsevich
Let be an unknown function in , and be its reconstruction from discrete Radon transform data, where is the data sampling rate. We study the resolution of…
Resolution analysis of inverting the generalized -dimensional Radon transform in from discrete data
Alexander Katsevich
Let denote the generalized Radon transform (GRT), which integrates over a family of -dimensional smooth submanifolds , $1\le…
On the spectral properties of the Hilbert transform operator on multi-intervals
Marco Bertola, Alexander Katsevich, Alexander Tovbis
Let be two multi-intervals with non-intersecting interiors. Consider the following operator $$A:\, L^2( J )\to L^2(E),\ (Af)(x) = \frac 1π\int_{ J } \frac {f(…
Analysis of resolution of tomographic-type reconstruction from discrete data for a class of distributions
Alexander Katsevich
Let , , be a piecewise smooth function with a jump discontinuity across a smooth surface . Let denote the Lambda tomography (LT) reconst…