Distributed Generalized Wirtinger Flow for Interferometric Imaging on Networks

TL;DR

This paper introduces a decentralized algorithm called DGWF for interferometric imaging over networks, which achieves centralized-level accuracy in image reconstruction through a distributed approach, leveraging low-rank matrix recovery theory.

Contribution

The paper develops DGWF, a novel primal-dual distributed algorithm for interferometric imaging, and provides theoretical convergence guarantees under the Regularity Condition.

Findings

DGWF converges geometrically for smooth functions.

DGWF achieves the same reconstruction quality as centralized methods.

Numerical simulations validate effectiveness across different network sizes.

Abstract

We study the problem of decentralized interferometric imaging over networks, where agents have access to a subset of local radar measurements and can compute pair-wise correlations with their neighbors. We propose a primal-dual distributed algorithm named Distributed Generalized Wirtinger Flow (DGWF). We use the theory of low rank matrix recovery to show when the interferometric imaging problem satisfies the Regularity Condition, which implies the Polyak-Lojasiewicz inequality. Moreover, we show that DGWF converges geometrically for smooth functions. Numerical simulations for single-scattering radar interferometric imaging demonstrate that DGWF can achieve the same mean-squared error image reconstruction quality as its centralized counterpart for various network connectivity and size.