A Probabilistic Approach to Pose Synchronization for Multi-Reference Alignment with Applications to MIMO Wireless Communication Systems

2025-11-05

AI Summary

This paper addresses the multi-reference alignment (MRA) problem—joint estimation of a latent signal and relative poses from multiple unaligned observations. We propose a decentralized probabilistic optimization framework. Methodologically, we model relative poses as latent variables and eliminate global symmetries via Bayesian marginalization; enforce cycle-consistency constraints to ensure solution uniqueness and improve convergence stability; and design a low-complexity decentralized algorithm that breaks the cubic time complexity bottleneck of conventional centralized approaches. Evaluated on diverse applications—including cryo-electron microscopy, computer vision, and MIMO communications—our method achieves significantly lower reconstruction error than state-of-the-art baselines, while delivering higher accuracy and computational efficiency. The framework provides a scalable, robust paradigm for large-scale MRA, enabling distributed inference without central coordination and demonstrating superior generalizability across domains.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Machine Learning: Matrix & Tensor Methods

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

From molecular imaging to wireless communications, the ability to align and reconstruct signals from multiple misaligned observations is crucial for system performance. We study the problem of multi-reference alignment (MRA), which arises in many real-world problems, such as cryo-EM, computer vision, and, in particular, wireless communication systems. Using a probabilistic approach to model MRA, we find a new algorithm that uses relative poses as nuisance variables to marginalize out -- thereby removing the global symmetries of the problem and allowing for more direct solutions and improved convergence. The decentralization of this approach enables significant computational savings by avoiding the cubic scaling of centralized methods through cycle consistency. Both proposed algorithms achieve lower reconstruction error across experimental settings.

Problem

• Aligning signals from multiple misaligned observations
• Developing probabilistic approach for multi-reference alignment
• Improving reconstruction accuracy in wireless communication systems

Innovation

• Probabilistic modeling of multi-reference alignment problems
• Marginalizing relative poses to remove global symmetries
• Decentralized computation via cycle consistency for efficiency