Related papers: An improved exact inversion formula for cone beam …
Several semianalytical approaches are now available for describing diffraction of a plane wave by the 2D (two dimensional) traction free isotropic elastic wedge. In this paper we follow Budaev and Bogy who reformulated the original…
In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray…
The first purpose of this paper is to solve completely the finite field cone restriction conjecture in four dimensions with $-1$ non-square. The second is to introduce a new approach to study incidence problems via restriction theory. More…
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish…
We consider the linearized electrical impedance tomography problem in two dimensions on the unit disk. By a linearization around constant coefficients and using a trigonometric basis, we calculate the linearized Dirichlet-to-Neumann…
The contour integration technique applied to calculate the optical conductivity tensor at finite temperatures in the case of layered systems within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker band…
Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is…
Cone-beam computed tomography (CBCT) offers advantages over conventional fan-beam CT in that it requires a shorter time and less exposure to obtain images. CBCT has found a wide variety of applications in patient positioning for…
Estimating the depth of omnidirectional images is more challenging than that of normal field-of-view (NFoV) images because the varying distortion can significantly twist an object's shape. The existing methods suffer from troublesome…
A novel mathematical approach has been developed to complete the inversion of the Biot-Savart law in one- and two-dimensional cases from measurements of the perpendicular component of the magnetic field using the well-developed…
Topo-Tomography (TT) is a synchrotron-based X-ray diffraction imaging technique used to characterize grain shape and crystal orientation in polycrystalline samples. This work aims to provide a decisive and fundamental understanding of 3D…
Currently, theory of ray transforms of vector and tensor fields is well developed, but the Radon transforms of such fields have not been fully analyzed. We thus consider linearly weighted and unweighted longitudinal and transversal Radon…
3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the…
In this paper I present three new results of astronomical interest concerning the theory of Abel inversion. 1) I show that in the case of a spatial emissivity that is constant on toroidal surfaces and projected along the symmetry axis…
It was recently realized that the polarization bases of the plane-wave modes in the integral representation of a light beam need to be determined by a degree of freedom arising from the divergence-free Maxwell's equation. This is a…
We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in…
A unified description of the free-space cylindrical vector beams is presented, which is an integral transformation solution to the vector Helmholtz equation and the transversality condition. The amplitude 2-form of the angular spectrum…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
In this article we propose a dynamic approach to complex vector reconstruction in the context of quantum tomography. There are two underlying assumptions behind our reasoning. The first one claims that the evolution of a d-level pure…