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The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the…

Analysis of PDEs · Mathematics 2021-09-01 Gang Bao , Yuantong Liu , Faouzi Triki

A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…

Analysis of PDEs · Mathematics 2020-10-13 Loc H. Nguyen , Qitong Li , Michael V. Klibanov

In this work we discuss the problem of identifying sound sources from pressure measurements with a Bayesian approach. The acoustics are modelled by the Helmholtz equation and the goal is to get information about the number, strength and…

Numerical Analysis · Mathematics 2019-01-16 Sebastian Engel , Dominik Hafemeyer , Christian Münch , Daniel Schaden

We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $\Omega$ from their values at scattered points $x_1,\dots,x_n\subset \Omega$. This problem typically arises when sampling acoustic…

Numerical Analysis · Mathematics 2014-04-04 Gilles Chardon , Albert Cohen , Laurent Daudet

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…

Analysis of PDEs · Mathematics 2016-07-25 Peijun Li , Ganghua Yuan

We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…

Numerical Analysis · Mathematics 2018-05-23 Mirza Karamehmedović , Adrian Kirkeby , Kim Knudsen

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

Analysis of PDEs · Mathematics 2026-02-24 Daniela Di Donato , Luca Rondi

This paper is concerned with an inverse random source problem for the one-dimensional stochastic Helmholtz equation with attenuation. The source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator…

Numerical Analysis · Mathematics 2020-09-30 Peijun Li , Xu Wang

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…

Analysis of PDEs · Mathematics 2018-01-18 Deyue Zhang , Yukun Guo , Jingzhi Li , Hongyu Liu

We consider the acoustic source imaging problems using multiple frequency data. Using the data of one observation direction/point, we prove that some information (size and location) of the source support can be recovered. A non-iterative…

Analysis of PDEs · Mathematics 2017-12-08 Ala Alzaalig , Guanghui Hu , Xiaodong Liu , Jiguang Sun

This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…

Numerical Analysis · Mathematics 2024-01-02 Hongxia Guo , Guanghui Hu

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…

Optimization and Control · Mathematics 2022-09-28 William W. Symes , Huiyi Chen , Susan E. Minkoff

The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…

Analysis of PDEs · Mathematics 2009-10-14 Yury Podlipenko , Yury Shestopalov , Vladimir Prishlyak

This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and…

Analysis of PDEs · Mathematics 2023-07-14 Peijun Li , Ying Liang

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…

Numerical Analysis · Mathematics 2024-04-19 Phuoc-Truong Huynh , Konstantin Pieper , Daniel Walter

Experimental aeroacoustics is concerned with the estimation of acoustic source power distributions, which are for instance caused by fluid structure interactions on scaled aircraft models inside a wind tunnel, from microphone array…

Numerical Analysis · Mathematics 2022-10-05 Roland Griesmaier , Hans-Georg Raumer

The paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end…

Analysis of PDEs · Mathematics 2019-11-05 Mozhgan Nora Entekhabi , Ajith Gunaratne

This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…

Numerical Analysis · Mathematics 2024-04-02 Mengjie Zhao , Suliang Si , Guanghui Hu

This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…

Analysis of PDEs · Mathematics 2025-03-14 Tianjiao Wang , Xiang Xu , Yue Zhao

This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang
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