A direct sampling method to an inverse medium scattering problem

2012 ◽  
Vol 28 (2) ◽  
pp. 025003 ◽  
Author(s):  
Kazufumi Ito ◽  
Bangti Jin ◽  
Jun Zou
Keyword(s):  
Sampling Method ◽  
Scattering Problem ◽  
Direct Sampling ◽  
Inverse Medium ◽  
Inverse Medium Scattering

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.

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

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

A Sampling Method to an Inverse Scattering Problem for Stationary Schrödinger Equation

2013 ◽  
Vol 275-277 ◽  
pp. 1585-1589
Author(s):  
Yuan Li ◽  
Ming Chen Yao ◽  
Chun Mei Wang ◽  
Fa Yong Zhang
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Sampling Method ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Potential Scattering ◽  
Stationary Schrödinger Equation ◽  
Direct Sampling

For an inverse potential scattering problem of stationary Schrödinger equation, we employ a direct sampling method to reconstruct the support of the potential. Compared with the general sampling method, the method we adopt is applicable even when the measured data (near-field data) are only available for one or several incident directions, and has the advantages of simple computation and insensitivity to noises. By the mathematical derivations, we conclude theoretically that for both two dimensional and three dimensional cases, this direct sampling method is feasible and efficient.

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.

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