Locating Multiple Multiscale Electromagnetic Scatterers by a Single Far-Field Measurement

Two inverse scattering schemes were recently developed in [J. Li, H. Liu, Z. Shang, and H. Sun, SIAM J. Appl. Math., 73 (2013), pp. 1721-1746] for locating multiple electromagnetic (EM) scatterers of small size and regular size compared to the detecting EM wavelength. Both schemes make use of a single far-field measurement. The scheme of locating regular-size scatterers requires a priori knowledge of the possible shapes, orientations, and sizes of the underlying scatterer components. In this paper, we extend that imaging scheme to a much more practical setting by relaxing the requirement on the orientations and sizes. We also develop an imaging scheme of locating multiple multiscale EM scatterers, which may include, at the same time, components of both regular size and small size. For the second scheme, a novel local resampling technique is developed. Furthermore, more robust and accurate reconstruction can be achieved for the second scheme if an additional far-field measurement is used. Rigorous mathematical justifications are provided, and numerical results are presented to demonstrate the effectiveness and the promising features of the proposed imaging schemes.