Related papers: Generalized V-line transforms in 2D vector tomogra…
We present a computational method for reconstructing a vector field on a convex polytope $\mathcal{P} \subset \mathbb{R}^d$ of arbitrary dimension from discrete samples. We specifically address the scenario where the vector field is subject…
The admissibility problem in integral geometry asks for which collections of affine subspaces the Radon transform remains injective. In the discrete setting, this becomes a purely combinatorial question about recovering a function on a…
In this paper, we consider the conical Radon transform on all cones with horizontal central axis whose vertices are on a straight line. We derive an explicit inversion formula for such transform. The inversion makes use of the vertical…
We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…
We introduce an analytic method which stably reconstructs both components of a (sufficiently) smooth, real valued, vector field compactly supported in the plane from knowledge of its Doppler transform and its first moment Doppler transform.…
In documents and graphics, contours are a popular format to describe specific shapes. For example, in the True Type Font (TTF) file format, contours describe vector outlines of typeface shapes. Each contour is often defined as a sequence of…
We outline a general methodology to infer the inductive velocity field vector in solar active regions. For the first time, both the field-aligned and the cross-field velocity components are reconstructed. The cross-field velocity solution…
We introduce a general framework for the reconstruction of vector-valued functions from finite and possibly noisy data, acquired through a known measurement operator. The reconstruction is done by the minimization of a loss functional…
We consider the renormalization of massive vector field interacting with charged scalar field in curved spacetime. Starting with the theory minimally coupled to external gravity and using the formulations with and without St\"uckelberg…
Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…
Tomography is the area of reconstructing objects from projections. Here we wish to reconstruct a set of cells in a two dimensional grid, given the number of cells in every row and column. The set is required to be an hv-convex polyomino,…
We calculate the one-loop divergences for different vector field models in curved spacetime. We introduce a classification scheme based on their degeneracy structure, which encompasses the well-known models of the non-degenerate vector…
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…
In this work we present the foundations of generalized scalar-tensor theories arising from vector bundle constructions, and we study the kinematic, dynamical and cosmological consequences. In particular, over a pseudo-Riemannian space-time…
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…
The light field reconstruction from the focal stack can be mathematically formulated as an ill-posed integral equation inversion problem. Although the previous research about this problem has made progress both in practice and theory, its…
The classical $\overline \partial$-method has been generalized recently [lnv], [lnv2] to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…
We introduce and discuss a new approach to the phase retrieval of fields radiated by continuous aperture sources having a circular support, which is of interest in many applications including the detection of shape deformations on reflector…