Related papers: Monotonicity-based regularization of inverse mediu…
We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of the scattered waves associated with incident plane waves sent from one direction but at multiple frequencies. We define, for each frequency,…
In this paper, we establish two sharp quantitative results for the direct and inverse time-harmonic acoustic wave scattering. The first one is concerned with the recovery of the support of an inhomogeneous medium, independent of its…
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…
We consider the wave scattering and inverse scattering in an inhomogeneous medium embedded a homogeneous droplet with a small size, which is modeled by a constant mass density and a small bulk modulus. Based on the Lippmann-Schwinger…
We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far…
This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
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…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded…
This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…
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…
This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
Inverse obstacle scattering is the recovery of an obstacle boundary from the scattering data produced by incident waves. This shape recovery can be done by iteratively solving a PDE-constrained optimization problem for the obstacle…
We consider an inverse shape problem for recovering an unknown simply supported obstacle in two dimensions from near--field point--source measurements for the biharmonic Helmholtz equation. The measured data consist of the scattered field…
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…
We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…
This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…
In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile.…