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 …

Inferring brain connectivity and structure in-vivo requires accurate estimation of the
orientation distribution function (ODF), which encodes key local tissue properties. However …

Comparing spherical probability distributions is of great interest in various fields, including
geology, medical domains, computer vision, and deep representation learning. The utility of …

Optimal Transport has received much attention in Machine Learning as it allows to compare
probability distributions by exploiting the geometry of the underlying space. However, in its …

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 …

We obtain new inversion formulas for the Funk type transforms of two kinds associated to
spherical sections by hyperplanes passing through a common point A which lies inside the n …

We study the spherical slice transform 𝔖 which assigns to a function f on the unit sphere Sn
in ℝ n+ 1 the integrals of f over cross-sections of Sn by k-dimensional affine planes passing …

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 …

We investigate analytic properties of the double Fourier sphere (DFS) method, which
transforms a function defined on the two-dimensional sphere to a function defined on the two …

We study non-geodesic Funk-type transforms on the unit sphere 𝕊 n in ℝ n+ 1 associated
with cross-sections of 𝕊 n by k-dimensional planes passing through an arbitrary fixed point …