Twofold subspace-based optimization method for solving inverse scattering problems

In this paper, we propose a twofold subspace-based optimization method to tackle the problem of determining the dielectric profile of extended scatterers. Based on the recently reported subspace-based optimization method, we further analyze the spectral property of the current-to-field mapping operator inside the domain of interest. By using this property, we find that it is possible to firstly restrict the induced current in some lower-dimensional subspace to efficiently generate a meaningful profile that could be used as the initial guess of the next step's optimization with a higher-dimensional current subspace. Such a scheme dramatically boosts the convergence rate of the optimization compared to the original subspace-based optimization method. Numerical simulations validate the twofold method and meanwhile show that it is quite robust against noise.