Exact Imaging of Extended Targets Using Multistatic Interferometric Measurements
arXiv:1905.10459 · doi:10.1109/TCI.2020.2967151
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.
arXiv comment16 pages, in revision for IEEE Transactions on Computational Imaging
References in corpus (7)
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
- High-Resolution Radar via Compressed Sensing
- Phase Retrieval via Wirtinger Flow: Theory and Algorithms
- MIMO Radar Using Compressive Sampling
- Convex recovery from interferometric measurements
- A Generalization of Wirtinger Flow for Exact Interferometric Inversion
- Kirchhoff migration without phases