Abstract
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.
Highlights
The electromagnetic inverse scattering problems (ISPs) are to reconstruct the geometric shape, constitutive parameters of the unknown scatterers by using the measured scattering data outside the domain of interest (DOI)
We investigate a wavelet-expansion based subspace regularization technique, namely, wavelet transform twofold subspace-based optimization method (WT-TSOM), on the unknowns for the inversion with contraction integral equation for inversion (CIE-I) to solve highly nonlinear ISPs
This paper presents a wavelet based twofold subspace-based optimization method, i.e., WT-TSOM, for solving highly nonlinear ISPs by using of the CIE-I model
Summary
The electromagnetic inverse scattering problems (ISPs) are to reconstruct the geometric shape, constitutive parameters of the unknown scatterers by using the measured scattering data outside the domain of interest (DOI). In [19], a hybrid regularization inversion method with TSOM and multiplicative regularization applied directly on the unknowns was proposed to solve the highly ISPs based on CIE-I, where it shows that the TV regularization can help to release the stringent subspace constraint from TSOM, could help to increase the resolvability of the inversion method Another regularization is investigated within the inversion model of CIE-I, i.e., the iterative multiscaling approach (IMSA), and it is shown that IMSA can help to stabilize the inversions with. We investigate a wavelet-expansion based subspace regularization technique, namely, wavelet transform twofold subspace-based optimization method (WT-TSOM), on the unknowns for the inversion with CIE-I to solve highly nonlinear ISPs. Instead of using Fourier bases, the wavelet bases are used to represent the induced currents for the CIE-I model within the TSOM frame.
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