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.

中文翻译：

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具有动态滤波的稀疏贝叶斯学习用于推断时变稀疏信号

许多信号处理应用需要估计时变稀疏信号，可能需要了解不完美的动力学模型。在本文中，我们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。该算法背后的关键思想，称为 SBL-DF，是将动态模型生成的信号预测和先前时间步长的估计合并到 SBL 概率模型的超先验中。所提出的算法是在线的，对不完美的动力学模型具有鲁棒性（由于动态信息通过高阶统计的传播），对某些不受欢迎的字典属性（例如一致性）具有鲁棒性（由于 SBL 框架的属性），允许使用任意动力学模型，并且需要比许多其他动态过滤算法更少的参数调整。我们还将快速边际似然 SBL 推理过程扩展到信息性超先验设置，以创建 SBL-DF 算法的特别有效版本。数值模拟表明，与标准 SBL 和其他动态滤波算法相比，SBL-DF 收敛速度更快，并且收敛到更准确的解决方案。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连贯性和列缩放结构时，我们表明 SBL-DF 优于最先进的算法。数值模拟表明，与标准 SBL 和其他动态滤波算法相比，SBL-DF 收敛速度更快，并且收敛到更准确的解决方案。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连贯性和列缩放结构时，我们表明 SBL-DF 优于最先进的算法。数值模拟表明，与标准 SBL 和其他动态滤波算法相比，SBL-DF 收敛速度更快，并且收敛到更准确的解决方案。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连贯性和列缩放结构时，我们表明 SBL-DF 优于最先进的算法。