Related papers: Inverse Radiative Transport with Local Data
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
We deal with a dynamical system \begin{align*} & u_{tt}-\Delta u+qu=0 && {\rm in}\,\,\,\Omega \times (0,T)\\ & u\big|_{t=0}=u_t\big|_{t=0}=0 && {\rm in}\,\,\,\overline \Omega\\ & \partial_\nu u = f && {\rm in}\,\,\,\partial\Omega \times…
In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…
An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
The radiative transfer equation (RTE) for polarized light accepts a convenient exponential solution when the absorption matrix commutes with its integral. We characterize some of the matrix depth variations which are compatible with the…
It is of great interest to solve the inverse problem of stationary radiative transport equation (RTE) in optical tomography. The standard way is to formulate the inverse problem into an optimization problem, but the bottleneck is that one…
The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of the so-called \textquotedblleft convexification" method, which…
We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility…
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…
We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, the exiting radiation is measured on an arc. The attenuation and scattering…
The inverse reflector problem aims to design a freeform reflecting surface that can direct the light from a specified source to produce the desired illumination in the target area, which is significant in the field of geometrical…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
Study of a simple single-trace transmission example shows how an extended source formulation of full-waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via…
In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…
This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…
In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…
Rotated reference frames offer fast algorithms for the radiative transport equation (RTE). We review the singular-eigenfunction approach and related numerical methods for the multi-dimensional RTE with rotated reference frames.
We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…
In this paper, a restricted transverse ray transform acting on vector and symmetric $m$-tensor fields is studied. We developed inversion algorithms using restricted transverse ray transform data to recover symmetric $m$-tensor fields in…