On the numerical solution of a three-dimensional inverse medium scattering problem

2001 ◽  
Vol 17 (6) ◽  
pp. 1743-1763 ◽  
Author(s):  
Thorsten Hohage
Keyword(s):  
Numerical Solution ◽  
Scattering Problem ◽  
Three Dimensional ◽  
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

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

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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