An FFT Twofold Subspace-Based Optimization Method for Solving Electromagnetic Inverse Scattering Problems

A fast Fourier transform (FFT) twofold subspace- based optimization method (TSOM) is proposed to solve electromagnetic inverse scattering problems. As mentioned in the original TSOM (Y. Zhong, et al, Inverse Probl., vol. 25, p. 085003, 2009), one is able to efficiently obtain a meaningful coarse result by constraining the induced current to a lower-dimensional subspace during the optimization, and use this result as the initial guess of the optimization with higher-dimensional current subspace. Instead of using the singular vectors to construct the current subspace as in the original TSOM, in this paper, we use discrete Fourier bases to construct a current subspace that is a good approximation to the original current subspace spanned by singular vectors. Such an approximation avoids the computationally burdensome singular value decomposition and uses the FFT to accomplish the construction of the induced current, which reduce the computational complexity and memory demand of the algorithm compared to the original TSOM. By using the new current subspace approximation, the proposed FFT-TSOM inherits the merits of the TSOM, better stability during the inversion and better robustness against noise compared to the SOM, and meanwhile has lower computational complexity than the TSOM. Numerical tests in the two-dimensional TM case and the three-dimensional one validate the algorithm.