# Exact Imaging of Extended Targets Using Multistatic Interferometric Measurements

## TL;DR

This paper introduces a new wave-based multistatic interferometric imaging method using Generalized Wirtinger Flow (GWF) that guarantees exact recovery of extended targets, enabling super-resolution imaging.

## Contribution

It develops a deterministic lifted forward model satisfying GWF conditions for exact multistatic radar imaging, with bounds on pixel spacing and sample complexity.

## Key findings

- GWF guarantees exact recovery under certain conditions.
- The method achieves super-resolution in multistatic radar imaging.
- Applicable to acoustics and geophysics imaging problems.

## Abstract

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.