Related papers: A reflection approach to the broken ray transform
We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.
We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas…
We show that there is non-uniqueness for the Calder{\'o}n problem with partial data for Riemannian metrics with H{\"o}lder continuous coefficients in dimension greater or equal than three. We provide simple counterexamples in the case of…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
In this paper we introduce and study a Bargmann-Radon transform on the real monogenic Bargmann module. This transform is defined as the projection of the real Bargmann module on the closed submodule of monogenic functions spanned by the…
We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of…
Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…
We consider weighted ray-transforms $P\_W$ (weighted Radon transforms along straight lines) in $\mathbb{R}^d, \, d\geq 2,$ with strictly positive weights $W$. We construct an example of such a transform with non-trivial kernel in the space…
We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with unbroken rays and for…
The colliding between an ultra-intense laser pulse with a high energy electron beam is not only an important source for high-brightness gamma-rays but also a powerful approach to exploit new physics in the exotic strong-field QED regime. In…
We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting that charged dopants locally suppress quantum reflection from…
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
The geometrical diffraction theory, in the sense of Keller,is here reconsidered as an obstacle problem in the Riemannian geometry. The first result is the proof of the existence and the analysis of the main properties of the diffracted…
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property $C$ and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)…
Understanding reflection remains a long-standing challenge in 3D reconstruction due to the entanglement of appearance and geometry under view-dependent reflections. In this work, we present the Pygmalion Effect in Vision, a novel framework…
Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem…
Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann…
This article presents extensions of the Cram{\'e}r-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions…
Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…