Related papers: Inverse Scattering for Dirac Equations Arising in …
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…
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.…
Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects…
For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from…
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 statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
Graphene quantum dots provide a platform for manipulating electron behaviors in two-dimensional (2D) Dirac materials. Most previous works were of the "forward" type in that the objective was to solve various confinement, transport and…
We consider the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by different models connected to the voltage-current map. Stationary as well as transient settings are discussed and a…
In this work, we construct the Born and inverse Born approximation and series to recover two function-valued coefficients in the Helmholtz equation for inverse scattering problems from the scattering data at two different frequencies. An…
Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…
In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
In this work, we consider the inverse electromagnetic scattering problem for a magneto-dielectric cylinder covering an impedance cylinder of arbitrary shape. We solve it by introducing a divide-and-conquer framework using specially designed…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
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…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…