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首页> 外文期刊>IEEE Transactions on Signal Processing >Sparse Bayesian Learning With Dynamic Filtering for Inference of Time-Varying Sparse Signals
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Sparse Bayesian Learning With Dynamic Filtering for Inference of Time-Varying Sparse Signals

机译：动态滤波的稀疏贝叶斯学习用于时变稀疏信号的推理

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摘要

Many signal processing applications require estimation of time-varying sparse signals, potentially with the knowledge of an imperfect dynamics model. In this paper, we propose an algorithm for dynamic filtering of time-varying sparse signals based on the sparse Bayesian learning (SBL) framework. The key idea underlying the algorithm, termed SBL-DF, is the incorporation of a signal prediction generated from a dynamics model and estimates of previous time steps into the hyperpriors of the SBL probability model. The proposed algorithm is online, robust to imperfect dynamics models (due to the propagation of dynamics information through higher-order statistics), robust to certain undesirable dictionary properties such as coherence (due to properties of the SBL framework), allows the use of arbitrary dynamics models, and requires the tuning of fewer parameters than many other dynamic filtering algorithms do. We also extend the fast marginal likelihood SBL inference procedure to the informative hyperprior setting to create a particularly efficient version of the SBL-DF algorithm. Numerical simulations show that SBL-DF converges much faster and to more accurate solutions than standard SBL and other dynamical filtering algorithms. In particular, we show that SBL-DF outperforms state of the art algorithms when the dictionary contains the challenging coherence and column scaling structure found in many practical applications.
机译：许多信号处理应用可能需要时变稀疏信号的估计，这可能需要了解不完善的动力学模型。本文提出了一种基于稀疏贝叶斯学习（SBL）框架的时变稀疏信号动态滤波算法。该算法的主要思想（称为SBL-DF）是将由动力学模型生成的信号预测和先前时间步长的估计合并到SBL概率模型的超优先级中。所提出的算法是在线的，对于不完善的动力学模型（由于通过高阶统计信息传播动力学信息）具有鲁棒性，对某些不希望的字典特性（如一致性）具有鲁棒性（由于SBL框架的特性），允许使用任意动态模型，并且比许多其他动态过滤算法所需的参数更少。我们还将快速边际似然SBL推理过程扩展到信息超优先级设置，以创建SBL-DF算法的特别有效版本。数值模拟表明，与标准的SBL和其他动态滤波算法相比，SBL-DF的收敛速度更快，解决方案更为准确。特别是，当字典包含在许多实际应用中发现的具有挑战性的一致性和列缩放结构时，我们证明SBL-DF的性能优于最新的算法。

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