Related papers: Trkalian fields: ray transforms and mini-twistors
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
Magnetic field is a powerful tool for the manipulation of material's electronic and optical properties. In the domain of transition metal dichalcogenide monolayers, it allows one to unveil the spin, valley, and orbital properties of…
We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…
In the past decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on…
A radial basis function (RBF) method based on matrix-valued kernels is presented and analyzed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is…
The ray transform $I$ integrates symmetric $m$-tensor field in $\mathbb{R}^n$ over lines. This transform in Sobolev spaces was studied in our earlier work where higher order Reshetnyak formulas (isometry relations) were established. The…
We study a particular broken ray transform on the Euclidean unit square and establish injectivity and stability for $C_{0}^{2}$ perturbations of the constant unit weight. Given an open subset $E$ of the boundary, we measure the attenuation…
Let $\bbK=\mathbb R, \mathbb C, \mathbb H$ be the field of real, complex or quaternionic numbers and $M_{p, q}(\bbK)$ the vector space of all $p\times q$-matrices. Let $X$ be the matrix unit ball in $M_{n-r, r}(\bbK)$ consisting of…
We relate a free scalar field in the Minkowski spacetime with a scalar field with a certain scaling dimension on a sphere of codimension two. This is realised by first performing a Radon transform of the ``bulk" field on the Minkowski space…
Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar- or vector-valued…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
Twist fields were introduced a few decades ago as a quantum counterpart to classical kink configurations and disorder variables in low dimensional field theories. In recent years they received a new incarnation within the framework of…
The paper contains a simple proof of the Finch-Patch-Rakesh inversion formula for the spherical mean Radon transform in odd dimensions. This transform arises in thermoacoustic tomography. Applications are given to the Cauchy problem for the…
We prove that a normal vector field along a curve in R3 is rotation minimizing (RM) if and only if it is parallel respect to the normal connection. This allows us to generalize all the results of RM vectors and frames to curves immersed in…
In this paper we characterise the optimal pointwise size and regularity estimates for the Dunkl Riesz transform kernel involving both the Euclidean metric and the Dunkl metric, where these two metrics are not equivalent. We further…
A method of computer simulation of Time-Resolved X-ray Diffraction (TRXD) in asymmetric Laue (transmission) geometry with an arbitrary propagating strain perpendicular to the crystal surface is presented. We present two case studies for…
The aim of this research is to reconstruct the 3D X-ray refractive index gradient maps by the proposed vector Radon transform and its inverse, assuming that the small-angle deviation condition is met. Theoretical analyses show that the…
For an image pixel information can be converted to the moments of some basis $Q_k$, e.g. Fourier-Mellin, Zernike, monomials, etc. Given sufficient number of moments pixel information can be completely recovered, for insufficient number of…
We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms.…