Related papers: A fast algorithm for radiative transport in isotro…
We present a transport equation for the incoherent propagation of radiation inside a quasi-resonant atomic gas at low temperature. The derivation is based on a generalized Bethe-Salpeter equation taking into account the motion of the atoms.…
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
We propose the redistribution-reconfiguration (red-rec) algorithm to prepare large configurations of atoms using arrays of dynamic optical traps. Red-rec exploits simple heuristics and exact subroutines to solve atom reconfiguration…
Orbital tomography has recently been established as a technique to reconstruct molecular orbitals directly from photoemission data using iterative phase retrieval algorithms. In this work, we present a detailed description of steps for…
In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of…
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
The Radiative Transfer Equation (RTE) is essential for solving the spatial distribution of light energy. It plays a crucial role in the link budget analysis of Underwater Wireless Optical Communication (UWOC). However, due to its complex…
We propose an approach for imaging in scattering media when large and diverse data sets are available. It has two steps. Using a dictionary learning algorithm the first step estimates the true Green's function vectors as columns in an…
Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known…
A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…
This paper introduces a directional multiscale algorithm for the two dimensional $N$-body problem of the Helmholtz kernel with applications to high frequency scattering. The algorithm follows the approach in [Engquist and Ying, SIAM Journal…
The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical…
A new, very fast method for 3D radiative transfer on fully threaded grids with arbitrarily high angular resolution is presented. The method uses completely cell-based discretization, and is ideally suited for problems with diffuse…
Context: The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to…
The fast marching algorithm, and its variants, solves numerically the generalized eikonal equation associated to an underlying riemannian metric. A major challenge for these algorithms is the non-isotropy of the riemannian metric.…
We propose a method of simulation that is based on the averaging of formal solutions of the transfer equation by taking the integral by the Monte Carlo method. This method is used to compute two models, which correspond to the limiting…
We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional…
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…