Compressive Online Robust Principal Component Analysis Via n-‘1 Minimization
Compressive Online Robust Principal Component Analysis Via n-‘1 Minimization
复制标题
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Huynh Van Luong
中科院分区：
文献类型：
--
作者：
Huynh Van Luong
-本工作考虑在线鲁棒主成分分析（RPCA）在时变分解问题，如视频前景背景分离。我们提出了一种压缩在线RPCA算法，该算法递归地将一系列数据向量（例如帧）分解为稀疏和低秩分量。与直接处理所有数据的传统批处理RPCA不同，我们的方法考虑每个数据向量（帧）的一小组测量。此外，我们的算法通过提出n - (cid:96) 1最小化方法，可以从先前的分解向量中合并多个先验信息。在每个时间实例中，该算法通过解决n - (cid:96) 1最小化问题来恢复稀疏向量，这不仅提高了向量的稀疏性，而且提高了它与多个先前恢复的稀疏向量的相关性，随后使用增量奇异值分解更新低秩分量。我们还建立了在静态或缓慢变化的低秩分量假设下保证成功压缩分离所需的测量次数的理论界限。我们通过数值实验和在线视频前背景分离实验对该算法进行了评价。实验结果表明，该方法优于现有方法。
—This work considers online robust principal component analysis (RPCA) in time-varying decomposition problems such as video foreground-background separation. We propose a compressive online RPCA algorithm that decomposes recursively a sequence of data vectors (e.g., frames) into sparse and low-rank components. Different from conventional batch RPCA, which processes all the data directly, our approach considers a small set of measurements taken per data vector (frame). Moreover, our algorithm can incorporate multiple prior information from previous decomposed vectors via proposing an n - (cid:96) 1 minimization method. At each time instance, the algorithm recovers the sparse vector by solving the n - (cid:96) 1 minimization problem—which promotes not only the sparsity of the vector but also its correlation with multiple previously-recovered sparse vectors—and, subsequently, updates the low-rank component using incremental singular value decomposition. We also establish theoretical bounds on the number of measurements required to guarantee successful compressive separation under the assumptions of static or slowly-changing low-rank components. We evaluate the proposed algorithm using numerical experiments and online video foreground-background separation experiments. The experimental results show that the proposed method outperforms the existing methods.