Decentralized Expectation Consistent Signal Recovery for Phase Retrieval

Abstract

In this study, we present a phase retrieval solution that aims to recover signals from noisy phaseless measurements. A recently proposed scheme known as generalized expectation consistent signal recovery (GEC-SR), has shown better accuracy, speed, and robustness than many existing methods. However, sensing high-resolution images with large transform matrices presents a computational burden for GEC-SR, thereby limiting its applications to areas, such as real-time implementation. Moreover, GEC-SR does not support distributed computing, which is an important requirement to modern computing. To address these issues, we propose a novel decentralized algorithm called & x201C;deGEC-SR & x201D; by leveraging the core framework of GEC-SR. deGEC-SR exhibits excellent performance similar to GEC-SR but runs tens to hundreds of times faster than GEC-SR. We derive the theoretical state evolution for deGEC-SR and demonstrate its accuracy using numerical results. Analysis allows quick generation of performance predictions and enriches our understanding on the proposed algorithm.