scholarly journals Improved TV-CS Approaches for Inverse Scattering Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. T. Bevacqua ◽  
L. Di Donato
Keyword(s):  
Compressive Sensing ◽  
Total Variation ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Problems ◽  
Piecewise Constant ◽  
Numerical Examples ◽  
Inverse Scattering Problems

Total Variation and Compressive Sensing (TV-CS) techniques represent a very attractive approach to inverse scattering problems. In fact, if the unknown is piecewise constant and so has a sparse gradient, TV-CS approaches allow us to achieve optimal reconstructions, reducing considerably the number of measurements and enforcing the sparsity on the gradient of the sought unknowns. In this paper, we introduce two different techniques based on TV-CS that exploit in a different manner the concept of gradient in order to improve the solution of the inverse scattering problems obtained by TV-CS approach. Numerical examples are addressed to show the effectiveness of the method.

scholarly journals An Efficient Technique for Solving Inhomogeneous Electromagnetic Inverse Scattering Problems

2020 ◽  
Vol 20 (1) ◽  
pp. 64-72 ◽  
Author(s):  
Mohamed Elkattan
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Scattered Data ◽  
Global Minimization ◽  
Scattering Problems ◽  
Inverse Scattering Problems ◽  
Cooling Schedules ◽  
Electromagnetic Inverse Scattering

The electromagnetic inverse scattering approach seeks to obtain the electric characteristics of a scatterer using information about the source and the scattered data. The inverse scattering problem usually suffers from limited knowledge about the scatterer used, which makes its solution more challenging than the forward problem. This paper presents an inversion approach to estimating the unknown electric properties of a two- and three-dimensional inhomogeneous scatterer. The presented approach considers the inverse scattering problem as a global minimization problem with a meshless forward formulation for the computation of the scattered electromagnetic field. Various simulated annealing cooling schedules are applied and assessed to solve the problem, and the results of several case studies are presented for both two- and three-dimensional electromagnetic inverse scattering problems.

scholarly journals Photonic-dispersion neural networks for inverse scattering problems

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Tongyu Li ◽  
Ang Chen ◽  
Lingjie Fan ◽  
Minjia Zheng ◽  
Jiajun Wang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Practical Significance ◽  
Single Shot ◽  
Inverse Mapping ◽  
Scattering Problems ◽  
Inverse Scattering Problems ◽  
Forward Mapping

AbstractInferring the properties of a scattering objective by analyzing the optical far-field responses within the framework of inverse problems is of great practical significance. However, it still faces major challenges when the parameter range is growing and involves inevitable experimental noises. Here, we propose a solving strategy containing robust neural-networks-based algorithms and informative photonic dispersions to overcome such challenges for a sort of inverse scattering problem—reconstructing grating profiles. Using two typical neural networks, forward-mapping type and inverse-mapping type, we reconstruct grating profiles whose geometric features span hundreds of nanometers with nanometric sensitivity and several seconds of time consumption. A forward-mapping neural network with a parameters-to-point architecture especially stands out in generating analytical photonic dispersions accurately, featured by sharp Fano-shaped spectra. Meanwhile, to implement the strategy experimentally, a Fourier-optics-based angle-resolved imaging spectroscopy with an all-fixed light path is developed to measure the dispersions by a single shot, acquiring adequate information. Our forward-mapping algorithm can enable real-time comparisons between robust predictions and experimental data with actual noises, showing an excellent linear correlation (R2 > 0.982) with the measurements of atomic force microscopy. Our work provides a new strategy for reconstructing grating profiles in inverse scattering problems.

scholarly journals Two-Step Extended Sampling Method for the Inverse Acoustic Source Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jiyu Sun ◽  
Yuhui Han
Keyword(s):  
Inverse Scattering ◽  
Sampling Method ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Indicator Function ◽  
Scattering Data ◽  
Acoustic Source ◽  
Scattering Problems ◽  
Linear Sampling Method ◽  
Ill Posed

Recently, a new method, called the extended sampling method (ESM), was proposed for the inverse scattering problems. Similar to the classical linear sampling method (LSM), the ESM is simple to implement and fast. Compared to the LSM which uses full-aperture scattering data, the ESM only uses the scattering data of one incident wave. In this paper, we generalize the ESM for the inverse acoustic source problems. We show that the indicator function of ESM, which is defined using the approximated solutions of some linear ill-posed integral equations, is small when the support of the source is contained in the sampling disc and is large when the source is outside. This behavior is similar to the ESM for the inverse scattering problem. Numerical examples are presented to show the effectiveness of the method.

DISCUSSION OF QUANTUM INVERSE SCATTERING PROBLEMS FOR COUPLED CHANNELS AT FIXED ENERGY

2011 ◽  
Vol 20 (08) ◽  
pp. 1765-1773 ◽  
Author(s):  
WERNER SCHEID ◽  
BARNABAS APAGYI
Keyword(s):  
Angular Momentum ◽  
Inverse Scattering ◽  
Nuclear Physics ◽  
Total Angular Momentum ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Practical Method ◽  
Scattering Problems ◽  
Coupled Channels ◽  
S Matrix

In nuclear physics, the inverse scattering problem for coupled channels at fixed energies searches for the coupling potentials by using the S matrix as information. On the basis of the Newton–Sabatier method we investigate the special case that the coupling is independent of the total angular momentum. We discuss transparent potentials and consider a principal, but not practical method for the solution of coupling potentials dependent on total angular momentum.

Numerical solution of the system of Marchenko integral equations

2021 ◽  
Vol 65 (3) ◽  
pp. 159-165
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Algebraic Equations ◽  
System Of Differential Equations ◽  
Scattering Problems ◽  
First Order ◽  
First Order Differential Equations

In this paper, inverse scattering problems for a system of differential equations of the first order are considered. The Marchenko approach is used to solve the inverse scattering problem. The system of Marchenko integral equations is reduced to a linear system of algebraic equations such that the solution of the resulting system yields to the unknown coefficients of the system of first-order differential equations. Illustrative examples are provided to demonstrate the preciseness and effectiveness of the proposed technique. The results are compared with the exact solution by using computer simulations.

scholarly journals Comparing Two Approaches for Point-Like Scatterer Detection

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Angela Dell’Aversano ◽  
Giovanni Leone ◽  
Raffaele Solimene
Keyword(s):  
Compressed Sensing ◽  
Inverse Scattering ◽  
Time Reversal ◽  
Mutual Coupling ◽  
Good Option ◽  
Scattering Problems ◽  
Numerical Examples ◽  
Inverse Scattering Problems ◽  
Reconstruction Methods

Many inverse scattering problems concern the detection and localisation of point-like scatterers which are sparsely enclosed within a prescribed investigation domain. Therefore, it looks like a good option to tackle the problem by applying reconstruction methods that are properly tailored for such a type of scatterers or that naturally enforce sparsity in the reconstructions. Accordingly, in this paper we compare the time reversal-MUSIC and the compressed sensing. The study develops through numerical examples and focuses on the role of noise in data and mutual coupling between the scatterers.

An iterative ensemble Kalman method for an inverse scattering problem in acoustics

2020 ◽  
Vol 34 (28) ◽  
pp. 2050312
Author(s):  
Zhaoxing Li
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Homogeneous Medium ◽  
Inverse Scattering Problem ◽  
Numerical Examples ◽  
Incident Waves

This paper studies an inverse problem of reconstructing a sound-soft obstacle from a homogeneous medium. We deal with it in the framework of statistical inversion and adopt an iterative ensemble Kalman algorithm to reconstruct the boundary. Some numerical examples show that the algorithm is effective and it can recover the shape of the boundary using one or several of the incident waves.

Far field patterns and inverse scattering problems for imperfectly conducting obstacles

1989 ◽  
Vol 106 (3) ◽  
pp. 553-569 ◽  
Author(s):  
T. S. Angell ◽  
David Colton ◽  
Rainer Kress
Keyword(s):  
Boundary Condition ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Impedance Boundary Condition ◽  
Far Field ◽  
Scattering Problems ◽  
Impedance Boundary ◽  
Field Patterns

AbstractWe first examine the class of far field patterns for the scalar Helmholtz equation in ℝ2 corresponding to incident time harmonic plane waves subject to an impedance boundary condition where the impedance is piecewise constant with respect to the incident direction and continuous with respect to x ε ∂ D where ∂ D is the scattering obstacle. We then examine the class of far field patterns for Maxwell's equations in subject to an impedance boundary condition with constant impedance. The results obtained are used to derive optimization algorithms for solving the inverse scattering problem.

Inverse Scattering Based on Proper Solution Space

2019 ◽  
Vol 27 (03) ◽  
pp. 1850033
Author(s):  
A. Hamad ◽  
M. Tadi
Keyword(s):  
Boundary Conditions ◽  
Inverse Scattering ◽  
Unknown Function ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Solution Space ◽  
Initial Guess ◽  
Proper Solution ◽  
New Approach ◽  
Numerical Examples

This paper is concerned with an inverse scattering problem in frequency domain, when the scattered field is governed by the Helmholtz equation. The algorithm is iterative in nature. It introduces a new approach which we refer to as proper solution space. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. The updating stage is accomplished by generating a set of functions that satisfy some of the required boundary conditions. We refer to this space as proper solution space. The correction to the assumed value can then be obtained by imposing the remaining boundary conditions. A number of numerical examples are used to study the applicability and effectiveness of the new approach.

scholarly journals Regularization and numerical solution of the inverse scattering problem using shearlet frames

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Gitta Kutyniok ◽  
Volker Mehrmann ◽  
Philipp C. Petersen
Keyword(s):  
Numerical Solution ◽  
Nonlinear Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Problems ◽  
Algorithmic Approach ◽  
Linearized Problem ◽  
Regularization Techniques ◽  
Two Space Dimensions

AbstractRegularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of cartoon-like functions. Since functions in this class are asymptotically optimally sparsely approximated by shearlet frames, we consider shearlets as a means for regularization. We analyze two approaches, namely solvers for the nonlinear problem and for the linearized problem obtained by the Born approximation. As example for the first class we study the acoustic inverse scattering problem, and for the second class, the inverse scattering problem of the Schrödinger equation. Whereas our emphasis for the linearized problem is more on the theoretical side due to the standardness of associated solvers, we provide numerical examples for the nonlinear problem that highlight the effectiveness of our algorithmic approach.

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