基于拉伸因子图的低复杂度贝叶斯稀疏信号算法研究

摘要/Abstract

摘要： 建立加性高斯白噪声的线性数学模型,针对此模型对基于稀疏贝叶斯学习的消息传递算法进行研究。对传统的因子图通过添加额外的硬约束节点得到改进的因子图,然后在改进的因子图中利用联合BP-MF规则,提出低复杂度的BP-MF SBL算法。为了进一步降低复杂度,在BP-MF SBL的基础上提出近似BP-MF SBL算法。仿真结果表明与向量形式的MF算法相比,所提方法复杂度低,且性能有所提升;与标量形式的MF算法相比,在复杂度相似的情况下,所提方法的性能更好。

关键词: BP-MF SBL算法, 低复杂度, 加性高斯白噪声, 拉伸因子图, 稀疏贝叶斯学习

Abstract: The linear mathematical model of additive Gauss white noise was established,and the message passing algorithm based on Sparse Bayesian learning was studied in this model.In this work,we modified the factor graph by adding some extra hard constraints which enables the use of combined belief propagation (BP) and MF message passing.This paper proposed a low complexity BP-MF SBL algorithm,based on which an approximate BP-MF SBL algorithm was also developed to further reduce the complexity.The BP-MF SBL algorithms show their merits compared with state-of-the-art MF SBL algorithms.They deliver even better performance with much lower complexity compared with the vector-form MF SBL algorithm and they significantly outperform the scalar-form MF SBL algorithm with similar complexity.

Key words: Additive Gauss white noise, BP-MF SBL algorithm, Low complexity, Sparse Bayesian learning, Stretched factor graph

中图分类号:

TP301

卞孝丽. 基于拉伸因子图的低复杂度贝叶斯稀疏信号算法研究[J]. 计算机科学, 2018, 45(6A): 135-139. https://doi.org/

BIAN Xiao-li. Low Complexity Bayesian Sparse Signal Algorithm Based on Stretched Factor Graph[J]. Computer Science, 2018, 45(6A): 135-139. https://doi.org/

参考文献

[1]DONOHO D L.Compressed sensing[J].IEEE Trans.Inform.Theory,2016,52(4):1289-1306. [2]WIPF D P,RAO B D.Sparse Bayesian learning for basis selection[J].IEEE Trans.Signal Processing,2014,52(8):2153-2164. [3]CHEN S,DONOHO D L,SAUNDERS M A.Atomic decomposition by basic pursuit[J].SIAM Journal on Scientific Computing,2008(1):33-61. [4]TROPP J A.Greed is good:algorithmic results for sparse approximation[J].IEEE Trans.Information Theory,2013:2231-2242. [5]TIPPING M E.Sparse Bayesian learning and the relevance vector machine[J].Journal of Machine Learning Research,2011,1:211-244. [6]TIPPING M E,FAUL A C.Fast marginal likelihood maximisation for sparse Bayesian models[C]∥Proc.9th International Workshop on Artificial Intelligence and Statistics.2003:3-6. [7]SHUTIN D,BUCHGRABER T,KULKARNI S R,et al.Fast variational sparse Bayesian learning with automatic relevance determination for superimposed signals[J].IEEE Trans.Signal Processing,2011,59(12):6257-6261. [8]PEDERSEN N L,MANCH N C N,BADIU M A,et al.Sparse estimation using Bayesian hierarchical prior modeling for real and complex linear models[J].Signal Processing,2015,115:94-109. [9]TAN X,LI J.Computationally efficient sparse Bayesian learning via belief propagation[C]∥2009 Conference Record of the Forty-Third Asilomar Conference on Signals,Systems and Computers,2009:1566-1570. [10]BARON D,SARVOTHAM S,BARANIUK R.Bayesian com- pressive sensing via belief propagation[J].IEEE Trans.Signal Processing,2010,58(1):269-280. [11]SOM S,SCHNITER P.Compressive imaging using approximate message passing and aMarkov-tree prior[J].IEEE Trans.Signal Processing,2012,60(7):3439-3448. [12]AL-SHOUKAIRI M,RAO B.Sparse Bayesian learning using approximate message passing[C]∥2014 48th Asilomar Confe-rence on Signals,Systems and Computers.2014:1957-1961. [13]XING E P,JORDAN M I,RUSSELL S.A generalized mean field algorithm for variational inference in exponential families[C]∥Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence(UAI’03).San Francisco,CA,USA,2013:583-591. [14]BISHOP C M,WINN J.Structured variational distributions in VIBES[C]∥Proceedings of Artificial Intelligence and Statistics.2003:3-6. [15]DAUWELS J.On variational message passing on factor graphs[C]∥Proc.IEEE International Symposium on InformationTheo-ry (ISIT 2007).2007:2546-2550. [16]PEDERSEN N L,MANCH N C N,SHUTIN D,et al.Application of Bayesian hierarchical prior modeling to sparse channel estimation[C]∥2007 IEEE International Conference on Communications (ICC 2012).2012:3487-3492. [17]HANSEN T L,J RGENSEN P B,BADIU M,et al.Joint sparse channel estimation and decoding:Continuous and discrete domain sparsity[J].arXiv:1507.02954. [18]RIEGLER E,KIRKELUND G E,MANCH N C N,et al.Merging belief propagation and the mean field approximation:A free energy approach[J].IEEE Trans.Inform.Theory,2013,59(1):588-602. [19]RANGAN S.Generalized approximate message passing for estimation with random linear mixing[C]∥Proc.IEEE Int.Symp.on Inform.Theory (ISIT 2011).2011:2168-2172. [20]PEDERSEN N L,MANCH N C N,FLEURY B H.Low complexity sparse Bayesian learning for channel estimation using generalized mean field[C]∥20th European Wireless Confe-rence.2014:838-843. [21]KSCHISCHANG F,FREY B,LOELIGER H A.Factor graphs and the sum-product algorithm[J].IEEE Trans.Inform.Theory,2001,47(2):498-519.

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