Wavelet Transform Subspace-Based Optimization Method for Inverse Scattering

Inspired by the new fast Fourier transform subspace-based optimization method (NFFT-SOM), wavelet transform subspace-based optimization method (WT-SOM) that represents the minor part of induced current by wavelet bases is proposed in this paper to solve the inverse scattering problem. This paper provides a guideline for choosing the appropriate bases for the minor part of induced current in the inverse problem, and it is shown that Daubechies 20 wavelet bases and Fourier bases are better choices than Daubechies 4 wavelet bases and Haar wavelet bases. Compared to NFFT-SOM, it is shown that WT-SOM can be used to improve the resolution of a specific region of a scatterer. By using only a part of the detail coefficients, the convergence rate of the algorithm can be greatly accelerated compared to using all the detail coefficients. For a piecewise constant scatterer, additive total variation (TV) regularization is used together with WT-SOM. We prove that TV-regularized WT-SOM has exactly the same performance when the contrast is represented by no matter natural pixels bases, Fourier bases, or wavelet bases.