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.

Evaluation of a Diffusion Coefficient Based on Proper Solution Space

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Yuanlong Wang ◽  
Abdalkaleg Hamad ◽  
Mohsen Tadi
Keyword(s):  
Diffusion Coefficient ◽  
Steady State ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Solution Space ◽  
Initial Guess ◽  
Proper Solution ◽  
Numerical Examples ◽  
Steady State Heat ◽  
Unknown Diffusion Coefficient

Abstract This note is concerned with the evaluation of the unknown diffusion coefficient in a steady-state heat conduction problem. The proposed method is iterative and, starting with an initial guess, updates the assumed value at every iteration. The updating stage is achieved by generating a set of functions that satisfy some of the required boundary conditions. The correction to the assumed value is then computed by imposing the remaining boundary conditions. Numerical examples are used to study the applicability of this method.

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.

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.

The Landweber Iteration for an Inverse Scattering Problem

1995 ◽  
Author(s):  
Martin Hanke ◽  
Frank Hettlich ◽  
Otmar Scherzer
Keyword(s):  
Numerical Solution ◽  
Inverse Scattering ◽  
Obstacle Problem ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Iteration Scheme ◽  
Far Field ◽  
Numerical Examples

Abstract A Landweber iteration scheme is presented for the numerical solution of an inverse obstacle problem. The method uses a recently obtained characterization of the Fréchet derivative of the far field operator and its adjoint. The performance of the method is illustrated by some numerical examples. Some theoretical aspects are pointed out to motivate the use of nonlinear Landweber iteration.

scholarly journals Bayesian Method for Shape Reconstruction in the Inverse Interior Scattering Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yujie Wang ◽  
Fuming Ma ◽  
Enxi Zheng
Keyword(s):  
Point Source ◽  
Inverse Scattering ◽  
Bayesian Method ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Shape Reconstruction ◽  
Closed Curve ◽  
Well Posedness ◽  
Numerical Examples ◽  
Scattered Fields

The inverse scattering problem of an interior cavity with three different boundary conditions is considered. Bayesian method is used to reconstruct the shape of the cavity from scattered fields incited by point source(s) and measured on a closed curve inside the cavity. We prove the well-posedness in Bayesian perspective and present numerical examples to show the viability of the method.

Reciprocity gap method for an interior inverse scattering problem

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Fang Zeng ◽  
Xiaodong Liu ◽  
Jiguang Sun ◽  
Liwei Xu
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Inhomogeneous Medium ◽  
Inverse Scattering ◽  
Interior Point ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Cauchy Data ◽  
Point Sources ◽  
Numerical Examples

AbstractWe consider an interior inverse scattering problem of reconstructing the shape of a cavity with inhomogeneous medium inside. We prove a uniqueness theorem for the inverse problem. Using Cauchy data on a curve inside the cavity due to interior point sources, we employ the reciprocity gap method to reconstruct the cavity. Numerical examples are provided to show the effectiveness of the method.

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