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

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.

Compressed Sensor Caching and Collaborative Sparse Data Recovery with Anchor Alignment

This work examines the compressed sensor caching problem in wireless sensor networks and devises efficient distributed sparse data recovery algorithms to enable collaboration among multiple caches. In this problem, each cache is only allowed to access measurements from a small subset of sensors within its vicinity to reduce both cache size and data acquisition overhead. To enable reliable data recovery with limited access to measurements, we propose a distributed sparse data recovery method, called the collaborative sparse recovery by anchor alignment (CoSR-AA) algorithm, where collaboration among caches is enabled by aligning their locally recovered data at a few anchor nodes. The proposed algorithm is based on the consensus alternating direction method of multipliers (ADMM) algorithm but with message exchange that is reduced by considering the proposed anchor alignment strategy. Then, by the deep unfolding of the ADMM iterations, we further propose the Deep CoSR-AA algorithm that can be used to significantly reduce the number of iterations. We obtain a graph neural network architecture where message exchange is done more efficiently by an embedded autoencoder. Simulations are provided to demonstrate the effectiveness of the proposed collaborative recovery algorithms in terms of the improved reconstruction quality and the reduced communication overhead due to anchor alignment.