scholarly journals Wavelet-Based Subspace Regularization for Solving Highly Nonlinear Inverse Scattering Problems with Contraction Integral Equation

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1760
Author(s):  
Lu Zhang ◽  
Zhenchao Ma ◽  
Kuiwen Xu ◽  
Yu Zhong
Keyword(s):  
Integral Equation ◽  
Inverse Scattering ◽  
Optimization Method ◽  
Good Choice ◽  
Scattering Problems ◽  
Regularization Technique ◽  
Wavelet Expansions ◽  
Inverse Scattering Problems ◽  
Highly Nonlinear ◽  
New Type

A wavelet transform twofold subspace-based optimization method (WT-TSOM) is proposed to solve the highly nonlinear inverse scattering problems with contraction integral equation for inversion (CIE-I). While the CIE-I is able to suppress the multiple scattering effects within inversion (without compromising the accuracy of the physics), proper regularization is needed. In this paper, we investigate a new type subspace regularization technique based on wavelet expansions for the induced currents. We found that the bior3.5 wavelet is a good choice to stabilize the inversions with the CIE-I model and in the meanwhile it also can rectify the contrast profile. Numerical tests against both synthetic and experimental data show that WT-TSOM is a promising regularization technique for inversion with CIE-I.

scholarly journals Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems

2019 ◽  
Vol 5 (2) ◽  
pp. 27 ◽  
Author(s):  
Yu Zhong ◽  
Kuiwen Xu
Keyword(s):  
Integral Equation ◽  
Inverse Scattering ◽  
Contraction Mapping ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Optimization Method ◽  
Scattering Problems ◽  
Physical Reason ◽  
Inverse Scattering Problems ◽  
Highly Nonlinear

Inverse scattering problems (ISPs) stand at the center of many important imaging applications, such as geophysical explorations, industrial non-destructive testing, bio-medical imaging, etc. Recently, a new type of contraction integral equation for inversion (CIE-I) has been proposed to tackle the two-dimensional electromagnetic ISPs, in which the usually employed Lippmann–Schwinger integral equation (LSIE) is transformed into a new form with a modified medium contrast via a contraction mapping. With the CIE-I, the multiple scattering effects, i.e., the physical reason for the nonlinearity in the ISPs, is substantially suppressed in estimating the modified contrast, without compromising physical modeling. In this paper, we firstly propose to implement this new CIE-I for the three-dimensional ISPs. With the help of the FFT type twofold subspace-based optimization method (TSOM), when handling the highly nonlinear problems with strong scatterers, those with higher contrast and/or larger dimensions (in terms of wavelengths), the performance of the inversions with CIE-I is much better than the ones with the LSIE, wherein inversions usually converge to local minima that may be far away from the solution. In addition, when handling the moderate scatterers (those the LSIE modeling can still handle), the convergence speed of the proposed method with CIE-I is much faster than the one with the LSIE. Secondly, we propose to relax the contraction mapping condition, i.e., different contraction mappings are used in updating contrast sources and contrast, and we find that the convergence can be further accelerated. Several numerical tests illustrate the aforementioned interests.

A diagonalized improved subspace-based optimization method for solving 2-D inverse scattering problems

2017 ◽  
Vol 59 (8) ◽  
pp. 2089-2095 ◽  
Author(s):  
Yulang Liu ◽  
Zhiqin Zhao ◽  
Xiaozhang Zhu ◽  
Wei Yang ◽  
Zaiping Nie ◽  
...  
Keyword(s):  
Inverse Scattering ◽  
Optimization Method ◽  
Scattering Problems ◽  
Inverse Scattering Problems
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