Related papers: Recovering the sources in the stochastic wave equa…
This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…
The reconstruction of multipolar acoustic or electromagnetic sources from their far-field signature plays a crucial role in numerous applications. Most of the existing techniques require dense multi-frequency data at the Nyquist sampling…
This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can…
A method is presented for the reconstruction of rotating monopole source distributions using acoustic pressures measured on a sideline parallel to the source axis. The method requires no \textit{a priori} assumptions about the source other…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
Inverse wave scattering aims at determining the properties of an object using data on how the object scatters incoming waves. In order to collect information, sensors are put in different locations to send and receive waves from each other.…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e. mass density and elastic Lam\'e parameters) of a weakly scattering medium from full-field data of scattered waves outside…
A new approach for solving the optical inverse problem of quantitative photoacoustic tomography is introduced, which interpolates between the well-known diffusion approximation and a radiative transfer equation based model. The proposed…
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…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…
Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…