This paper investigates the influence of the test dipole on the resolution of the multiple signal classification (MUSIC) imaging method applied to the electromagnetic inverse scattering problem of determining the locations of a collection of small objects embedded in a known background medium. Based on the analysis of the induced electric dipoles in eigenstates, an algorithm is proposed to determine the test dipole that generates a pseudo-spectrum with enhanced resolution. The amplitudes in three directions of the optimal test dipole are not necessarily in phase, i.e., the optimal test dipole may not correspond to a physical direction in the real three-dimensional space. In addition, the proposed test-dipole-searching algorithm is able to deal with some special scenarios, due to the shapes and materials of objects, to which the standard MUSIC does not apply.
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.
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