Related papers: Uniqueness for a seismic inverse source problem mo…

We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field…

Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the…

This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…

This paper studies the numerical solution of traveling singular sources problems. In such problems, a big challenge is the sources move with different speeds, which are described by some ordinary differential equations. A…

A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…

This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally…

In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background…

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

This paper is concerned with inverse source problems for the time-dependent Lam\'e system in an unbounded domain corresponding to the exterior of a bounded cavity or the full space $\R^3$. If the time and spatial variables of the source…

We study the uniqueness and accuracy of the numerical solution of the problem of reconstruction of the shape and trajectory of a reflecting obstacle moving in an inhomogeneous medium from travel times, start and end points, and initial…

This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives…

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…

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…

It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…

This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the…

We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…