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Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…

Numerical Analysis · Mathematics 2015-06-19 Tian Ding , Kui Ren

This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…

Analysis of PDEs · Mathematics 2018-08-01 Deyue Zhang , Yukun Guo , Jingzhi Li , Hongyu Liu

We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…

Numerical Analysis · Mathematics 2017-08-11 Ke Chen , Qin Li , Li Wang

This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface…

Numerical Analysis · Mathematics 2018-04-09 Guanghui Hu , Xiaoli Liu , Bo Zhang , Haiwen Zhang

We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…

Analysis of PDEs · Mathematics 2015-05-13 Tilmann Glimm

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…

Analysis of PDEs · Mathematics 2017-11-02 Li Jingzhi , Liu Hongyu , Sun Hongpeng

We demonstrate that simultaneous reconstruction of scattering and absorption of a mesoscopic system using angularly-resolved measurements of scattered light intensity is possible. Image reconstruction is realized based on the algebraic…

Optics · Physics 2011-01-07 Lucia Florescu , John C. Schotland , Vadim A. Markel

This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…

Numerical Analysis · Mathematics 2025-11-04 Hao Gu , Tianjiao Wang , Xiang Xu , Yue Zhao

Anisotropic two-dimensional diffraction signals encode additional structural information, including atom-pair angular distributions, beyond conventional isotropic scattering. However, experimental constraints such as beam stops result in…

Chemical Physics · Physics 2026-04-06 Yanwei Xiong , Martin Centurion

We study the reconstruction of the attenuation and absorption coefficients in a stationary linear transport equation from knowledge of albedo operator in dimension $n\geq 3$ on a Riemannian manifold in the presence of a magnetic field. We…

Analysis of PDEs · Mathematics 2013-10-01 Yernat M. Assylbekov , Yang Yang

Although travelling faster than the speed of light in vacuum is not physically allowed, the analogous bound in medium can be exceeded by a moving particle. For an electron in dielectric material this leads to emission of photons which is…

Analysis of PDEs · Mathematics 2021-10-18 Antti Kujanpää

We consider the problem of reconstruction of Cauchy data for the wave equation in $\mathbb{R}^1$ by the measurements of its solution on the boundary of the finite interval. This is a one-dimensional model for the multidimensional problem of…

Analysis of PDEs · Mathematics 2025-05-26 D. Langemann , A. S. Mikhaylov , V. S. Mikhaylov

We present two theorems describing analytic left-inverses of partial X-ray transforms. The first theorem concerns X-ray data collected with an arbitrary distribution of parallel projections; it contains a convolution-backprojection formula…

Medical Physics · Physics 2025-07-01 Murdock G. Grewar

We solve the Cauchy problem of the Ward model in light-cone coordinates using the inverse spectral (scattering) method. In particular we show that the solution can be constructed by solving a $2\times 2$ local matrix Riemann-Hilbert problem…

High Energy Physics - Theory · Physics 2007-05-23 A. S. Fokas , T. A. Ioannidou

A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…

Numerical Analysis · Mathematics 2025-10-20 Oliver Dorn

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor field in a two dimensional strictly convex set is considered. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation…

Analysis of PDEs · Mathematics 2024-12-06 David Omogbhe

The construction of exact solutions for radiative transfer in a plane-parallel medium has been addressed by Hemsch and Ferziger in 1972 for a partial frequency redistribution model of the formation of spectral lines consisting in a linear…

Solar and Stellar Astrophysics · Physics 2024-10-31 Hélène Frisch

We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…

Analysis of PDEs · Mathematics 2020-04-24 Walton Green , Shitao Liu

This work studies the problem of content-based image retrieval, specifically, texture retrieval. It focuses on feature extraction and similarity measure for texture images. Our approach employs a recently developed method, the so-called…

Information Retrieval · Computer Science 2015-06-02 Alexander Sagel , Dominik Meyer , Hao Shen