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Related papers: Stability for time-dependent inverse transport

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In this paper, we study the inverse random source scattering problem for the biharmonic Schrodinger equation in two and three dimensions. The driven source is assumed to be a generalized microlocally isotropic Gaussian random function whose…

Analysis of PDEs · Mathematics 2024-12-24 Tianjiao Wang , Xiang Xu , Yue Zhao

In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we…

Analysis of PDEs · Mathematics 2023-05-25 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…

Optimization and Control · Mathematics 2025-02-18 Kaiwen Shi

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Numerical Analysis · Mathematics 2022-03-14 Lu Zhao , Heping Dong , Fuming Ma

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…

Analysis of PDEs · Mathematics 2011-01-24 Tim J. P. M. Op 't Root , Christiaan C. Stolk , Maarten V. de Hoop

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

Numerical Analysis · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

Dynamical Systems · Mathematics 2015-05-19 Gary Froyland , Naratip Santitissadeekorn , Adam Monahan

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

In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space variable but also on the time variable. More precisely, we attempt to stably and…

Analysis of PDEs · Mathematics 2018-10-05 Mourad Bellassoued , Ibtissem Ben Aïcha

We present and experimentally verify a matrix approach for determining how to optimally sculpt an input wavefront both in space and time for any desired wave-control functionality, irrespective of the complexity of the wave scattering. We…

Applied Physics · Physics 2023-08-08 Clément Ferise , Philipp del Hougne , Matthieu Davy

In these lectures I give an introduction to the time-dependent approach to inverse scattering, that has been developed recently. The aim of this approach is to solve various inverse scattering problems with time-dependent methods that…

Mathematical Physics · Physics 2007-05-23 Ricardo Weder

Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…

Optimization and Control · Mathematics 2025-05-30 Tran T. A. Nghia , Huy N. Pham , Nghia V. Vo

We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements.

Analysis of PDEs · Mathematics 2007-05-23 Eva Sincich

We consider the problem of reconstructing the position and the time-dependent optical properties of a linear dispersive medium from OCT measurements. The medium is multi-layered described by a piece-wise inhomogeneous refractive index. The…

Numerical Analysis · Mathematics 2024-02-23 Peter Elbau , Leonidas Mindrinos , Leopold Veselka

When a signal is emitted from a source, recorded by an array of transducers, time reversed and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency,…

Disordered Systems and Neural Networks · Physics 2007-05-23 George Papanicolaou , Leonid Ryzhik , Knut Solna

Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…

Signal Processing · Electrical Eng. & Systems 2024-04-05 Nguyen T. Thao , Dominik Rzepka , Marek Miskowicz

Motivated by recent studies of the phenomenon of Coherent Perfect Absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as…

Disordered Systems and Neural Networks · Physics 2020-07-15 Mohammed Osman , Yan V. Fyodorov

We are interested in the identification of a Generalized Impedance Boundary Condition from the far--fields created by one or several incident plane waves at a fixed frequency. We focus on the particular case where this boundary condition is…

Numerical Analysis · Mathematics 2013-07-23 Laurent Bourgeois , Nicolas Chaulet , Houssem Haddar

We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…

Systems and Control · Electrical Eng. & Systems 2023-08-28 Sifeddine Benahmed , Romain Postoyan , Mathieu Granzotto , Lucian Buşoniu , Jamal Daafouz , Dragan Nešić

Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…

Analysis of PDEs · Mathematics 2023-11-29 General Ozochiawaeze