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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…
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 demonstrate a compact, cost-effective snapshot spectral imaging system named Aperture Diffraction Imaging Spectrometer (ADIS), which consists only of an imaging lens with an ultra-thin orthogonal aperture mask and a mosaic filter sensor,…
Hyperspectral image (HSI) deconvolution is a challenging ill-posed inverse problem, made difficult by the data's high dimensionality.We propose a parameter-parsimonious framework based on a low-rank Canonical Polyadic Decomposition (CPD) of…
We propose a direct imaging method based on the reverse time migration to reconstruct extended obstacles in the half space with finite aperture elastic scattering data at a fixed frequency. We prove the resolution of the reconstruction…
Existing deep learning-based hyperspectral image (HSI) classification works still suffer from the limitation of the fixed-sized receptive field, leading to difficulties in distinctive spectral-spatial features for ground objects with…
In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
In this paper we provide a mathematical model for imaging an anisotropic, orthotropic medium with Polarization-Sensitive Optical Coherence Tomography (PS-OCT). The imaging problem is formulated as an inverse scattering problem in three…
Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier…
This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…
This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…
Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…
We consider one-dimensional inverse scattering in attenuating media where both the reflectivity and loss distributions are unknown. Mathematically, this corresponds to recovering the coefficients of a damped wave operator, or equivalently,…
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The…