Theoretical and Numerical Validations of the Bifocusing Method for Identifying Small Objects with Incomplete MSR Matrices

This paper concerns the application of the Bifocusing Method (BFM) for imaging small, well-separated dielectric objects within a two-dimensional homogeneous domain using an zero-padded incomplete multi-static response (MSR) matrix. A core challenge in this constrained measurement setup is the presence of an interference term that could obscure target localization. To address this, we theoretically prove that the disturbing term of the imaging function is strictly bounded above by 0.2438, thereby guaranteeing the unique identification of targets without the interference overshadowing the dominant localization term. Extensive numerical simulations across various frequencies and diverse target properties validate these theoretical findings. The results demonstrate that the BFM-based imaging function robustly localizes targets despite substantial missing data.