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Approximate Message Passing for Structured Affine Rank Minimization Problem

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Bibliographic Details
Title: Approximate Message Passing for Structured Affine Rank Minimization Problem
Authors: Yangqing Li, Changchuan Yin, Wei Chen, Zhu Han
Source: IEEE Access, Vol 5, Pp 10093-10107 (2017)
Publisher Information: IEEE, 2017.
Publication Year: 2017
Collection: LCC:Electrical engineering. Electronics. Nuclear engineering
Subject Terms: Affine rank minimization (ARM), structured low-rank matrix recovery, approximate message passing (AMP), belief propagation, graphical models, sum-product algorithm (SPA), Electrical engineering. Electronics. Nuclear engineering, TK1-9971
Description: The topic of the rank minimization problem with affine constraints has been well studied in recent years. However, in many applications the data can exhibit other structures beyond simply being low rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current affine rank minimization (ARM) methods. In this paper, we propose a novel approximate message passing (AMP)-based approach that is capable of capturing additional structures in the matrix entries, and can be implemented in a wide range of applications with little or no modification. Using probabilistic low-rank factorization, we derive our generalized AMP-based algorithm as an approximation of the loopy belief propagation algorithm. In addition, we apply a rank selection strategy and an expectation-maximization estimation strategy that adaptively obtain the optimal value of the algorithmic parameters. Then, we discuss the specializations of our proposed algorithm to the applications of structured ARM problems, such as compressive hyperspectral imaging and compressive video surveillance. Simulation results with both synthetic and real data demonstrate that the proposed algorithm yields the state-of-the-art reconstruction performance while maintaining competitive computational complexity.
Document Type: article
File Description: electronic resource
Language: English
ISSN: 2169-3536
Relation: https://ieeexplore.ieee.org/document/7936453/; https://doaj.org/toc/2169-3536
DOI: 10.1109/ACCESS.2017.2710179
Access URL: https://doaj.org/article/3f0fa652d4444fcf81b59e98d8c0db2c
Accession Number: edsdoj.3f0fa652d4444fcf81b59e98d8c0db2c
Database: Directory of Open Access Journals
Description
Abstract:The topic of the rank minimization problem with affine constraints has been well studied in recent years. However, in many applications the data can exhibit other structures beyond simply being low rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current affine rank minimization (ARM) methods. In this paper, we propose a novel approximate message passing (AMP)-based approach that is capable of capturing additional structures in the matrix entries, and can be implemented in a wide range of applications with little or no modification. Using probabilistic low-rank factorization, we derive our generalized AMP-based algorithm as an approximation of the loopy belief propagation algorithm. In addition, we apply a rank selection strategy and an expectation-maximization estimation strategy that adaptively obtain the optimal value of the algorithmic parameters. Then, we discuss the specializations of our proposed algorithm to the applications of structured ARM problems, such as compressive hyperspectral imaging and compressive video surveillance. Simulation results with both synthetic and real data demonstrate that the proposed algorithm yields the state-of-the-art reconstruction performance while maintaining competitive computational complexity.
ISSN:21693536
DOI:10.1109/ACCESS.2017.2710179