Performance Analysis of Convex LRMR based Passive SAR Imaging

TL;DR

This paper analyzes a convex low-rank matrix recovery method for passive SAR imaging, demonstrating conditions for exact reconstruction, super-resolution capabilities, and the relation to phaseless imaging through theoretical analysis and simulations.

Contribution

The paper provides a theoretical performance analysis of the convex LRMR method for passive SAR, establishing conditions for exact recovery and super-resolution, and linking it to phaseless imaging.

Findings

Exact reconstruction guaranteed under certain pixel spacing conditions.

Method achieves super-resolution at high center frequencies.

Phaseless imaging is a special case of the proposed approach.

Abstract

Passive synthetic aperture radar (SAR) uses existing signals of opportunity such as communication and broadcasting signals. In our prior work, we have developed a low-rank matrix recovery (LRMR) method that can reconstruct scenes with extended and densely distributed point targets, overcoming shortcomings of conventional methods. The approach is based on correlating two sets of bistatic measurements, which results in a linear mapping of the tensor product of the scene reflectivity with itself. Recognizing this tensor product as a rank-one positive semi-definite (PSD) operator, we pose passive SAR image reconstruction as a LRMR problem with convex relaxation. In this paper, we present a performance analysis of the convex LRMR-based passive SAR image reconstruction method. We use the restricted isometry property (RIP) and show that exact reconstruction is guaranteed under the condition that the pixel spacing or resolution satisfies a certain lower bound. We show that for sufficiently large center frequencies, our method provides superior resolution than that of Fourier based methods, making it a super-resolution technique. Additionally, we show that phaseless imaging is a special case of our passive SAR imaging method. We present extensive numerical simulation to validate our analysis.