scholarly journals Solving a 1-D inverse medium scattering problem using a new multi-frequency globally strictly convex objective functional

2020 ◽  
Vol 28 (5) ◽  
pp. 693-711
Author(s):  
Nguyen T. Thành ◽  
Michael V. Klibanov
Keyword(s):  
Global Convergence ◽  
Error Estimate ◽  
Scattering Problem ◽  
Projection Algorithm ◽  
New Approach ◽  
Numerical Examples ◽  
Strictly Convex ◽  
Inverse Medium ◽  
Inverse Medium Scattering ◽  
Objective Functional

AbstractWe propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is proved. We also prove the global convergence of the gradient projection algorithm and derive an error estimate. Numerical examples are presented to illustrate the performance of the proposed algorithm.

Convexity of a discrete Carleman weighted objective functional in an inverse medium scattering problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Trung Thành
Keyword(s):  
Finite Number ◽  
Scattering Problem ◽  
One Dimensional ◽  
Globally Convergent ◽  
Convergent Method ◽  
Inverse Medium ◽  
Inverse Medium Scattering ◽  
Objective Functional

AbstractWe investigate a globally convergent method for solving a one-dimensional inverse medium scattering problem using backscattering data at a finite number of frequencies. The proposed method is based on the minimization of a discrete Carleman weighted objective functional. The global convexity of this objective functional is proved.

scholarly journals Globally Strictly Convex Cost Functional for a 1-D Inverse Medium Scattering Problem with Experimental Data

2017 ◽  
Vol 77 (5) ◽  
pp. 1733-1755 ◽  
Author(s):  
Michael V. Klibanov ◽  
Aleksandr E. Kolesov ◽  
Lam Nguyen ◽  
Anders Sullivan
Keyword(s):  
Experimental Data ◽  
Scattering Problem ◽  
Cost Functional ◽  
Strictly Convex ◽  
Convex Cost ◽  
Inverse Medium ◽  
Inverse Medium Scattering

Numerical solution of an inverse medium scattering problem with a stochastic source

2010 ◽  
Vol 26 (7) ◽  
pp. 074014 ◽  
Author(s):  
Gang Bao ◽  
Shui-Nee Chow ◽  
Peijun Li ◽  
Haomin Zhou
Keyword(s):  
Numerical Solution ◽  
Scattering Problem ◽  
Inverse Medium ◽  
Inverse Medium Scattering

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 Application of a Deep Neural Network to Phase Retrieval in Inverse Medium Scattering Problems

Computation ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 56
Author(s):  
Soojong Lim ◽  
Jaemin Shin
Keyword(s):  
Neural Network ◽  
Refractive Index ◽  
Optical Fibers ◽  
Deep Neural Network ◽  
Phase Retrieval ◽  
Scattering Problem ◽  
Scattering Problems ◽  
Retrieval Problem ◽  
Inverse Medium ◽  
Inverse Medium Scattering

We address the inverse medium scattering problem with phaseless data motivated by nondestructive testing for optical fibers. As the phase information of the data is unknown, this problem may be regarded as a standard phase retrieval problem that consists of identifying the phase from the amplitude of data and the structure of the related operator. This problem has been studied intensively due to its wide applications in physics and engineering. However, the uniqueness of the inverse problem with phaseless data is still open and the problem itself is severely ill-posed. In this work, we construct a model to approximate the solution operator in finite-dimensional spaces by a deep neural network assuming that the refractive index is radially symmetric. We are then able to recover the refractive index from the phaseless data. Numerical experiments are presented to illustrate the effectiveness of the proposed model.

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