标题： 通过l1最小化动态过滤时变稀疏信号 显示英文标题

标题： Dynamic Filtering of Time-Varying Sparse Signals via l1 Minimization

摘要： 尽管稀疏信号模型的重要性以及高维流数据的日益普及，但用于动态过滤时变稀疏信号的算法相对较少。 在现有的算法中，能够提供强大性能保证的更少。 本文研究了两种基于高效l1优化方法的稀疏信号动态过滤算法。 我们首先介绍了一种简单的算法（BPDN-DF），当系统动态已知时，该算法表现良好。 然后引入了一种新颖的第二个算法（RWL1-DF），该算法比BPDN-DF计算复杂度更高，但在实际应用中表现更好，特别是在系统动态模型不准确的情况下。 通过使用分层概率数据模型，并在稀疏推理过程中传播前一个估计的高阶统计量（类似于卡尔曼滤波），实现了对模型不准确性的鲁棒性。 我们在模拟数据以及自然视频序列上展示了这些算法的特性。 总的来说，本文提出的算法代表了对时变稀疏信号动态过滤算法的首次强大性能分析，同时也在此新兴应用中达到了最先进的性能。 显示英文摘要

摘要： Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer still provide strong performance guarantees. This paper examines two algorithms for dynamic filtering of sparse signals that are based on efficient l1 optimization methods. We first present an analysis for one simple algorithm (BPDN-DF) that works well when the system dynamics are known exactly. We then introduce a novel second algorithm (RWL1-DF) that is more computationally complex than BPDN-DF but performs better in practice, especially in the case where the system dynamics model is inaccurate. Robustness to model inaccuracy is achieved by using a hierarchical probabilistic data model and propagating higher-order statistics from the previous estimate (akin to Kalman filtering) in the sparse inference process. We demonstrate the properties of these algorithms on both simulated data as well as natural video sequences. Taken together, the algorithms presented in this paper represent the first strong performance analysis of dynamic filtering algorithms for time-varying sparse signals as well as state-of-the-art performance in this emerging application.