Related papers: Radon transform and kinetic equations in tomograph…
In this work we consider the Conical Radon Transform, which integrates a function on $\R^n$ over families of circular cones. Transforms of this type are known to arise naturally as models of Compton camera imaging and single-scattering…
We interpret the setting for a Radon transform as a submanifold of the space of generalized functions, and compute its extrinsic curvature: it is the Hessian composed with the Radon transform.
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
The crossing properties of the matrix elements of non-local operators, parameterized by Generalized Parton Distribution, are considered. They are especially simple in terms of the Double Distributions which are common for the various…
We introduce several possible generalizations of tomography for quadratic surfaces. We analyze different types of elliptic, hyperbolic and hybrid tomograms. In all cases it is possible to consistently define the inverse tomographic map. We…
Radon transform is a type of transform which is used in image processing to transfer the image into intercept-slope coordinate. Its diagonal properties made it appropriate for some applications which need processes in different degrees.…
A Radon-type transform called a cone transform that assigns to a given function its integral over various sets of cones has arisen in the last decade in the context of the study of Compton cameras used in Single Photon Emission Computed…
This paper is devoted to a Radon-type transform arising in a version of Photoacoustic Tomography that uses integrating circular detectors. We show that the transform can be decomposed into the spherical Radon transform and the…
The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of…
We study classical continuous systems with singular distributions of velocities. Radon measures with the infinite mass give these distributions. Positions of particles in such systems are no longer usual configurations in the location…
We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of…
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…
We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a support theorem that generalizes Helgason's support theorem for…
The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic…
We describe a classical thermodynamic model that reproduces the main features of the solid hydrogen phase diagram. In particular, we show how the general structure types that are found by electronic structure calculations and the quantum…
We study the Radon transform in the plane in parallel geometry possibly undersampled in the angular variables. We study resolution, aliasing artifacts, and edge recovery.
We study the Gaussian Radon transform in the classical Wiener space of Brownian motion. We determine explicit formulas for transforms of Brownian functionals specified by stochastic integrals. A Fock space decomposition is also established…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…