2017/01/10 by Yanting Ma, Ma, Yanting, Yue M. Lu +3 · 1 citation
Computer Science · Engineering · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1701.02578
This document contains complete details of the previous version (i.e., arXiv:1701.02578v1), which was accepted for publication in ICASSP 2017
openalex publication_date 2017/01/10 · arxiv created 2017/01/30 · arxiv updated 2017/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Solving a large-scale regularized linear inverse problem using multiple processors is important in various real-world applications due to the limitations of individual processors and constraints on data sharing policies. This paper focuses on the setting where the matrix is partitioned column-wise. We extend the algorithmic framework and the theoretical analysis of approximate message passing (AMP), an iterative algorithm for solving linear inverse problems, whose asymptotic dynamics are characterized by state evolution (SE). In particular, we show that column-wise multiprocessor AMP (C-MP-AMP) obeys an SE under the same assumptions when the SE for AMP holds. The SE results imply that (i) the SE of C-MP-AMP converges to a state that is no worse than that of AMP and (ii) the asymptotic dynamics of C-MP-AMP and AMP can be identical. Moreover, for a setting that is not covered by SE, numerical results show that damping can improve the convergence performance of C-MP-AMP.