Dynamic Filtering of Time-Varying Sparse Signals via $ell _1$ Minimization
Dynamic Filtering of Time-Varying Sparse Signals via $ell _1$ Minimization
复制标题
通过 $ell _1$ 最小化动态过滤时变稀疏信号
DOI：
--
复制
发表时间：
2015
影响因子：
5.4
通讯作者：
C. Rozell
中科院分区：
文献类型：
--
作者：
Adam S. Charles;A. Balavoine;C. Rozell
尽管稀疏信号模型的重要性和日益流行的高维流数据，有相对较少的算法动态滤波的时变稀疏信号。在现有的算法中，很少有算法能够提供强有力的性能保证。本文研究了两种基于高效的F11优化方法的稀疏信号动态滤波算法。首先，我们提出了一个简单的算法（BPDN-DF），工作良好，当系统的动态是准确的分析。然后，我们介绍了一种新的第二种算法（RWL 1-DF），这是更复杂的计算比BPDN-DF，但在实践中表现更好，特别是在系统动力学模型是不准确的情况下。通过使用分层概率数据模型和在稀疏推理过程中从先前估计（类似于卡尔曼滤波）传播高阶统计来实现对模型不准确性的鲁棒性。我们证明了这些算法的性能模拟数据以及自然的视频序列。两者合计，本文提出的算法代表了第一次强大的性能分析的动态滤波算法随时间变化的稀疏信号，以及国家的最先进的性能，在这个新兴的应用。
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 timevarying 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.