Robust Distributed Phase Retrieval for Multi-View Compressive Networked Sensing With Outliers

TL;DR

This paper introduces a distributed algorithm for multi-view compressive phase retrieval in sensor networks, enabling local sparse signal recovery despite outliers and limited data sharing, with proven theoretical guarantees and simulation validation.

Contribution

It presents a novel two-stage distributed reconstruction method that recovers global signal amplitude and local sparse signals without sharing raw data, handling outliers effectively.

Findings

Perfect global amplitude recovery under mild conditions

Exact local signal reconstruction in noise-free scenarios

Effective performance demonstrated through simulations

Abstract

This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the global sparse vector. The goal is to enable each sensor to recover its observable sparse signal when measurements are corrupted by outliers. To achieve reliable local signal recovery with limited data access, we propose a distributed reconstruction algorithm that enables collaboration among sensor devices without the need to share individual raw data. The proposed scheme employs a two-stage approach that first recovers the amplitude of the global signal (at a central server) and subsequently estimates the observable nonzero signal entries (at each local device). Our analytic results show that perfect global signal amplitude recovery can be achieved under mild conditions on the support size of sparse outliers and the view blockage level. In addition, the exact reconstruction of locally observed signal components is shown to be attainable in the noise-free case by solving a binary optimization problem, subject to a mild requirement on the structure of the sensing matrix. Computer simulations are provided to illustrate the effectiveness of the proposed scheme.