Inverse Scattering Research Articles

Full statistics of regularized local energy density in a freely expanding Kipnis–Marchioro–Presutti gas

Abstract We combine the Macroscopic Fluctuation Theory and the Inverse Scattering Method to determine the full long-time statistics of the energy density u ( x , t ) averaged over a given spatial interval, U = 1 2 L ∫ − L L d x u ( x , t ) , in a freely expanding Kipnis–Marchioro–Presutti (KMP) lattice gas on the line, following the release at t = 0 of a finite amount of energy at the origin. In particular, we show that, as time t goes to infinity at fixed L, the large deviation function of U approaches a universal, L-independent form when expressed in terms of the energy content of the interval | x | < L . A key part of the solution is the determination of the most likely configuration of the energy density at time t, conditional on U.

Bayesian Compressive Sensing With Variational Inference and Wavelet Tree Structure for Solving Inverse Scattering Problems

Bayesian Compressive Sensing With Variational Inference and Wavelet Tree Structure for Solving Inverse Scattering Problems

A Direct Sampling Method Based on the Green’s Function for Time-Dependent Inverse Scattering Problems

A Direct Sampling Method Based on the Green’s Function for Time-Dependent Inverse Scattering Problems

A Novel Time-Domain Direct Sampling Approach for Inverse Scattering Problems in Acoustics

A Novel Time-Domain Direct Sampling Approach for Inverse Scattering Problems in Acoustics

Phaseless inverse scattering with a parametrized spatial spectral volume integral equation for finite scatterers in the soft x-ray regime

Soft x-ray wafer-metrology experiments are characterized by low signal-to-noise ratios and lack phase information, which both cause difficulties with the accurate three-dimensional profiling of small geometrical features of structures on a wafer. To this end, we extend an existing phase-based inverse-scattering method to demonstrate a sub-nanometer and noise-robust reconstruction of the targets by synthetic soft x-ray scatterometry experiments. The targets are modeled as three-dimensional finite dielectric scatterers embedded in a planarly layered medium, where a scatterer’s geometry and spatial permittivity distribution are described by a uniform polygonal cross section along its height. Each cross section is continuously parametrized by its vertices and homogeneous permittivity. The combination of this parametrization of the scatterers and the employed Gabor frames ensures that the underlying linear system of the spatial spectral Maxwell solver is continuously differentiable with respect to the parameters for phaseless inverse-scattering problems. In synthetic demonstrations, we demonstrate the accurate and noise-robust reconstruction of the parameters without any regularization term. Most of the vertex parameters are retrieved with an error of less than λ/13 with λ=13.5nm, when the ideal sensor model with shot noise detects at least five photons per sensor pixel. This corresponds to a signal-to-noise ratio of 3.5 dB. These vertex parameters are retrieved with an accuracy of λ/90 when the signal-to-noise ratio is increased to 10 dB, or approximately 100 photons per pixel. The material parameters are retrieved with errors ranging from 0.05% to 5% for signal-to-noise ratios between 10 dB and 3.5 dB.

Full inverse Compton Scattering: Total transfer of energy and momentum from electrons to photons

In this article we discuss a peculiar regime of Compton Scattering that assures the maximum transfer of energy and momentum from free electrons propagating in vacuum to the scattered photons. We name this regime Full Inverse Compton Scattering (FICS) because it is characterized by the maximum and full energy loss of the electrons in collision with photons: up to 100% of the electron kinetic energy is indeed transferred to the photon. In the case of relativistic electrons, characterized by a large Lorentz factor (γ≫1), FICS regime corresponds to an incident photon energy equal to mec22, i.e. approximately 255.5 keV. We interpret such an astonishing result as FICS being the time reversal of direct Compton Scattering of very energetic photons (of energy much greater than mec2) onto atomic electrons. Although the cross section of Compton scattering is decreasing with the energy of the incident photon, making the process less probable with respect to other reactions (pair production, nuclear reactions, etc.) when high energetic photons are bombarding a target, the kinematics straightforwardly implies that the back-scattered photons would have an energy reaching asymptotically mec22. FICS is instead the unique suitable working point in Compton scattering for achieving the total transfer of (kinetic) energy exactly from the electron to the photon. Experiencing transitions from the initial momentum to zero in the laboratory system, in FICS the electron is also subject to very large negative acceleration; this fact can lead to possible experiments of sensing the Unruh temperature and related photon bath. On the other side of the energy dynamic range, low relativistic electrons can be completely stopped by moderate energy photons (tens of keV), leading to full exchange of temperature between electron clouds and photon baths. Cosmic gamma ray sources can be affected in their evolution by this peculiar FICS regime of Compton scattering.

Uniqueness criteria for inverse scattering problem in terms of transmission matrix in boundary condition for a first order system of ordinary differential equations

The inverse scattering problem (ISP) involves the recovery of the matrix coefficient of a first-order system on the half-line from its scattering matrix. Specifically, when the matrix coefficient exhibits a triangular structure, the system possesses a Volterra-type integral transformation operator at infinity. This transformation operator facilitates the determination of the scattering matrix on the half-line through matrix Riemann-Hilbert factorization. Solving the ISP on the half-line entails reducing it to an ISP on the whole line for the considered system. This reduction involves extending the coefficients to the whole line by zero. The uniqueness criteria in terms of transmission matrix in boundary condition for the ISP is also established.

Semantic-Electromagnetic Inversion With Pretrained Multimodal Generative Model.

Across diverse domains of science and technology, electromagnetic (EM) inversion problems benefit from the ability to account for multimodal prior information to regularize their inherent ill-posedness. Indeed, besides priors that are formulated mathematically or learned from quantitative data, valuable prior information may be available in the form of text or images. Besides handling semantic multimodality, it is furthermore important to minimize the cost of adapting to a new physical measurement operator and to limit the requirements for costly labeled data. Here, these challenges are tackled with a frugal and multimodal semantic-EM inversion technique. The key ingredient is a multimodal generator of reconstruction results that can be pretrained, being agnostic to the physical measurement operator. The generator is fed by a multimodal foundation model encoding the multimodal semantic prior and a physical adapter encoding the measured data. For a new physical setting, only the lightweight physical adapter is retrained. The authors' architecture also enables a flexible iterative step-by-step solution to the inverse problem where each step can be semantically controlled. The feasibility and benefits of this methodology are demonstrated for three EM inverse problems: a canonical two-dimensional inverse-scattering problem in numerics, as well as three-dimensional and four-dimensional compressive microwave meta-imaging experiments.

Nonautonomous Volterra Series Expansion of the Variable Phase Approximation and its Application to the Nucleon-Nucleon Inverse Scattering Problem

Abstract In this paper, the nonlinear Volterra series expansion is extended and used to describe certain types of nonautonomous differential equations related to the inverse scattering problem in nuclear physics. The nonautonomous Volterra series expansion lets us determine a dynamic, polynomial approximation of the variable phase approximation (VPA), which is used to determine the phase shifts from nuclear potentials through first-order nonlinear differential equations. By using the first-order Volterra expansion, a robust approximation is formulated to the inverse scattering problem for weak potentials and/or high energies. The method is then extended with the help of radial basis function neural networks by applying a nonlinear transformation on the measured phase shifts to be able to model the scattering system with a linear approximation given by the first-order Volterra expansion. The method is applied to describe the ${}^1S_0$ NN potentials in neutron+proton scattering below 200 MeV laboratory kinetic energies, giving physically sensible potentials and below $1\%$ averaged relative error between the recalculated and the measured phase shifts.

Tree internal defects detection method based on ResNet improved subspace optimization algorithm

The erosion behavior of trunk borers leads to the destruction of trunk structure and the formation of internal defects, which significantly impacts the ecological and economic value of trees. Traditional non-destructive testing (NDT) methods are costly and have low resolution, whereas electromagnetic NDT methods are more suitable for high-resolution detection and imaging. However, solving the highly nonlinear electromagnetic inverse scattering problems (ISPs) for small-sized defects with high contrast is challenging. Therefore, this paper proposes an improved subspace optimization algorithm based on a ResNet network called SOM-ResNet. SOM-ResNet incorporates physical principles into deep learning networks by simulating the iterative process of induced current and contrast, thereby enhancing its ability to accurately detect small objects with high contrast. Experimental results demonstrate that SOM-ResNet outperforms single inversion algorithms in detecting complex scatterers with small to medium-sized targets, validating its excellent performance.

Enhanced Deep Learning Approach Based on the Conditional Generative Adversarial Network for Electromagnetic Inverse Scattering Problems

Enhanced Deep Learning Approach Based on the Conditional Generative Adversarial Network for Electromagnetic Inverse Scattering Problems

Soliton groups and extreme wave occurrence in simulated directional sea waves

The evolution of nonlinear wave groups that can be associated with long-lived soliton-type structures is analyzed, based on the data of numerical simulation of irregular deep-water gravity waves with spectra typical to the ocean and different directional spreading. A procedure of the windowed Inverse Scattering Transform, which reveals wave sequences related to envelope solitons of the nonlinear Schrödinger equation, is proposed and applied to the simulated two-dimensional surfaces. The soliton content of waves with different directional spreading is studied in order to estimate its dynamical role, including characteristic lifetimes. Statistical features of the solitonic part of the water surface are analyzed and compared with the wave field on average. It is shown that intense wave patterns that persist for tens of wave periods can emerge in stochastic fields of relatively long-crested waves. They correspond to regions of locally enhanced on average waves with reduced kurtosis. This eventually leads to realization of locally extreme wave conditions compared to the general background. Although intense soliton-like groups may be detected in short-crested irregular waves as well, they possess much shorter lateral sizes, quickly disperse, and do not influence the local statistical wave properties.

A Kernel Machine Learning for Inverse Source and Scattering Problems

A Kernel Machine Learning for Inverse Source and Scattering Problems

Multiple Pole Solutions of the Hirota Equation Under Nonzero Boundary Conditions by Inverse Scattering Method

Multiple Pole Solutions of the Hirota Equation Under Nonzero Boundary Conditions by Inverse Scattering Method

Virtual Experiments via LSM for Quantitative 2-D Inverse Scattering: Challenges and Opportunities

Virtual Experiments via LSM for Quantitative 2-D Inverse Scattering: Challenges and Opportunities

2-D Electromagnetic Scattering and Inverse Scattering From Anisotropic Objects Under TE Illumination Solved by the Hybrid SIM/SEM

2-D Electromagnetic Scattering and Inverse Scattering From Anisotropic Objects Under TE Illumination Solved by the Hybrid SIM/SEM

Inverse Scattering for the Biharmonic Wave Equation with a Random Potential

Inverse Scattering for the Biharmonic Wave Equation with a Random Potential

Algorithms for Solving the Inverse Scattering Problem for the Manakov Model

Algorithms for Solving the Inverse Scattering Problem for the Manakov Model

Deep Neural Network-Oriented Indicator Method for Inverse Scattering Problems Using Partial Data

We consider the inverse scattering problem to reconstruct an obstacle using partial far-field data due to one incident wave. A simple indicator function, which is negative inside the obstacle and positive outside of it, is constructed and then learned using a deep neural network (DNN). The method is easy to implement and effective as demonstrated by numerical examples. Rather than developing sophisticated network structures for the classical inverse operators, we reformulate the inverse problem as a suitable operator such that standard DNNs can learn it well. The idea of the DNN-oriented indicator method can be generalized to treat other partial data inverse problems.

A Physics-Induced Deep Learning Scheme for Electromagnetic Inverse Scattering

A Physics-Induced Deep Learning Scheme for Electromagnetic Inverse Scattering