Related papers: Universal inversion formulas for recovering a func…
In this article we study the inverse problem of determining a semilinear term appearing in an elliptic equation from boundary measurements. Our main objective is to develop flexible and general theoretical results that can be used for…
In this paper, we propose a unified theoretical and practical spherical approximation framework for functional inverse problems on the hypersphere. More specifically, we consider recovering spherical fields directly in the continuous domain…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
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…
A general method for analytic inversion in integral geometry is proposed. All classical and some new reconstruction formulas of Radon-John type are obtained by this method. No harmonic analysis and PDE is used.
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…
The paper presents a new and simple range characterization for the spherical mean transform of functions supported in the unit ball in even dimensions. It complements the previous work of the same authors, where they solved an analogous…
We consider the Neumann version of the spherical mean value operator and its variants in the space of smooth functions, distributions and compactly supported ones. Surjectivity and range characterization issues are addressed from the…
We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…
A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settings, the nature of this anisotropy may be…
In this paper, we consider inverse shape problems coming from diffuse optical tomography and inverse scattering. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an…
The Funk--Minkowski transform ${\mathcal F}$ associates a function $f$ on the sphere ${\mathbb S}^2$ with its mean values (integrals) along all great circles of the sphere. Thepresented analytical inversion formula reconstruct the unknown…
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and…
3D reconstruction plays an increasingly important role in modern photogrammetric systems. Conventional satellite or aerial-based remote sensing (RS) platforms can provide the necessary data sources for the 3D reconstruction of large-scale…
We consider the problem of recovering a complete (i.e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb{R}^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse.…
In this paper, we introduce a computational framework for recovering a high-resolution approximation of an unknown function from its low-resolution indirect measurements as well as high-resolution training observations by merging the…
In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm,…