Type: Other
Publication Date: 2014-01-01
Citations: 9
DOI: https://doi.org/10.1090/conm/615/12264
Consider the scattering of a time-harmonic plane wave incident on a two-scale heterogeneous medium, which consists of scatterers that are much smaller than the wavelength and extended scatterers that are comparable to the wavelength. In addition to the standard inverse obstacle scattering prob- lem, i.e., to image the shape of extended scatterers as well as the location of the point scatterers where strong multiple scattering are present, there are a few other interesting issues such as imaging a target in a cluttered environment without resolving the clutters, and increasing the effective aperture by utilizing the multiple scattering between extended scatterers and point scatterers whose location are known. Some preliminary computational study will be given in this paper. To simulate the wave propagation in the heterogeneous medium with both point and extended scatterers, a generalized Foldy-Lax formulation and a physically based block Gauss-Seidel iterative method are used to solve the two-scale multiple scattering problem. Based on the singular value decom- position of the response matrix constructed from the far-field pattern, imaging functions are designed to visualize the location of the point scatterers and the shape of the extended obstacle scatterers. The method leads to a direct imag- ing algorithm which is simple and efficient since no direct solver or iteration is needed. The imaging functions are robust with respect to the measure- ment noise. Numerical experiments are presented for uniformly and randomly distributed point scatterers and multiple extended obstacle scatterers in both two- and three-dimensional cases.