  In this paper, we present a novel approach that can exactly recover extended
targets in wave-based multistatic interferometric imaging, based on Generalized
Wirtinger Flow (GWF) theory [1]. Interferometric imaging is a generalization of
phase retrieval, which arises from cross-correlation of measurements from pairs
of receivers in multistatic configuration. Unlike standard Wirtinger Flow, GWF
theory guarantees exact recovery for arbitrary lifted forward models that
satisfy the restricted isometry property over rank-1, positive semi-definite
(PSD) matrices with a sufficiently small restricted isometry constant (RIC). To
this end, we design a deterministic, lifted forward model for interferometric
multistatic radar satisfying the exact recovery conditions of the GWF theory.
Our results quantify a lower limit on the pixel spacing and the minimal sample
complexity for exact multistatic radar imaging via GWF. We provide a numerical
study of our RIC and pixel spacing bounds, which shows that GWF can achieve
exact recovery with super-resolution. While our primary interest lies in radar
imaging, our method is also applicable to other multistatic wave-based imaging
problems such as those arising in acoustics and geophysics.
