Data recovery: from limited-aperture to full-aperture
For researchers in inverse scattering, this work provides methods to enhance reconstruction quality when only limited-aperture data is available, though the improvements are incremental.
This paper addresses the problem of recovering full-aperture far field data from limited-aperture measurements in inverse scattering. Numerical results demonstrate partial recovery of missing data and improved scatterer reconstruction.
The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\em limited-aperture} measurement is available. In this paper, we perform some elementary study to recover data that can not be measured directly. To be precise, we aim at recovering the {\em full-aperture} far field data from {\em 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 {\em full-aperture} MSR. The recovered data is tested by a recently proposed direct sampling method and the factorization method. The numerical results show the possibility to recover, at least partially, the missing data and consequently improve the reconstruction of the scatterer.