Related papers: Untangling the nonlinearity in inverse scattering …
Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…
We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence,…
The current study aims to evaluate and investigate the development of projection-based reduced-order models (ROMs) for efficient and accurate RDE simulations. Specifically, we focus on assessing the projection-based ROM construction…
Scattering hinders the passage of light through random media and consequently limits the usefulness of optical techniques for sensing and imaging. Thus, methods for increasing the transmission of light through such random media are of…
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
We develop a Reduced Order Model (ROM) for a Large Eddy Simulation (LES) approach that combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
Our objective is to estimate the unknown compositional input from its output response through an unknown system after estimating the inverse of the original system with a training set. The proposed methods using artificial neural networks…
In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…
An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…
Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…
Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…
We have shown that the wave scattering by a soliton occurs in a peculiar way. The nonlinear interaction leads to the generation of waves with frequencies that are multiples of the frequency of the incident wave, minus the frequency of the…
Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by the presence of a detector,…
We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed and nonlinear, and the iterative…
Inverse scattering in layered media has a wide range of applications, examples including geophysical exploration, medical imaging, and remote sensing. In this paper, we develop a selective focusing method for identifying multiple unknown…
The 3-d inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. The main difference with the conventional inverse scattering problems is that only the…
We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin…
The image reconstruction of chromophore concentrations using Diffuse Optical Tomography (DOT) data can be described mathematically as an ill-posed inverse problem. Recent work has shown that the use of hyperspectral DOT data, as opposed to…