Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport
on the line. More precisely, sliced optimal transport is the concatenation of the well-known …

Sliced optimal transport, which is basically a Radon transform followed by one-dimensional
optimal transport, became popular in various applications due to its efficient computation. In …

Abstract The Funk-Radon transform assigns to a function defined on the unit sphere its
integrals along all great circles of the sphere. In this paper, we consider a frame …

Since the invention of Compton camera imaging, the conical Radon transform, which maps
a given function defined on 3-dimensional Euclidean space to its surface integrals over …

The singular value decomposition going with many problems in medical imaging, non-
destructive testing, geophysics, etc is of central importance. Unfortunately the effective …

The Funk--Minkowski transform ${\mathcal F} $ associates a function $ f $ on the sphere
${\mathbb S}^ 2$ with its mean values (integrals) along all great circles of the sphere …

WestudythenonuniquenessproblemforRado… directions. In the early days of the application
of computed tomography, they caused some confusion about the possible information …

In this study, we derive two new inversion formulae for the n+ 1-dimensional conical Radon
transform that integrates a given n+ 1-dimensional function on the upper half space over all …

A spherical Radon transform that averages a function over all spheres centered on a given
sphere is related to not only pure but also applied mathematics topics. Especially, the …

With well-selected data, homogeneous diffusion inpainting can reconstruct images from
sparse data with high quality. While 4K colour images of size 3840× 2160 can already be …