Data recovery in inverse scattering: From limited-aperture to full-aperture

Abstract

Inverse scattering has been an active research area for the past thirty years. While very successful in many cases, progress has lagged when only limited-aperture measurement is available. In this paper, we perform some elementary study to recover data that can not be measured directly. In particular, we aim at recovering the full-aperture far field data from limited-aperture measurement. Due to the reciprocity relation, the multi-static response matrix (MSR) has a symmetric structure. Using the Green's formula and single layer potential, we propose two schemes to recover full-aperture MSR. The recovered data is tested by a recently proposed direct sampling method and the factorization method. Numerical results show that it is possible to, at least, partially recover the missing data and consequently improve the reconstruction of the scatterer.