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On the Applications of Robust PCA in Image and Video Processing

机译：鲁棒PCA在图像和视频处理中的应用

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Robust principal component analysis (RPCA) via decomposition into low-rank plus sparse matrices offers a powerful framework for a large variety of applications such as image processing, video processing, and 3-D computer vision. Indeed, most of the time these applications require to detect sparse outliers from the observed imagery data that can be approximated by a low-rank matrix. Moreover, most of the time experiments show that RPCA with additional spatial and/or temporal constraints often outperforms the state-of-the-art algorithms in these applications. Thus, the aim of this paper is to survey the applications of RPCA in computer vision. In the first part of this paper, we review representative image processing applications as follows: 1) low-level imaging such as image recovery and denoising, image composition, image colorization, image alignment and rectification, multifocus image, and face recognition; 2) medical imaging such as dynamic magnetic resonance imaging (MRI) for acceleration of data acquisition, background suppression, and learning of interframe motion fields; and 3) imaging for 3-D computer vision with additional depth information such as in structure from motion (SfM) and 3-D motion recovery. In the second part, we present the applications of RPCA in video processing which utilize additional spatial and temporal information compared to image processing. Specifically, we investigate video denoising and restoration, hyperspectral video, and background/foreground separation. Finally, we provide perspectives on possible future research directions and algorithmic frameworks that are suitable for these applications.
机译：通过分解为低秩加稀疏矩阵的强大主成分分析（RPCA）为各种应用（例如图像处理，视频处理和3D计算机视觉）提供了强大的框架。确实，这些应用大多数时候都需要从观察到的图像数据中检测稀疏离群值，这些数据可以通过低秩矩阵来近似。此外，大多数时间实验表明，具有附加空间和/或时间约束的RPCA在这些应用中通常优于最新的算法。因此，本文的目的是调查RPCA在计算机视觉中的应用。在本文的第一部分中，我们回顾了代表性的图像处理应用程序，如下所示：1）低级成像，例如图像恢复和去噪，图像合成，图像着色，图像对齐和校正，多焦点图像和人脸识别； 2）医学成像，例如动态磁共振成像（MRI），用于加速数据采集，背景抑制和帧间运动场的学习； 3）具有附加深度信息的3-D计算机视觉成像，例如运动（SfM）和3-D运动恢复的结构。在第二部分中，我们介绍了RPCA在视频处理中的应用，与图像处理相比，它利用了额外的空间和时间信息。具体来说，我们研究视频降噪和恢复，高光谱视频以及背景/前景分离。最后，我们提供了适合这些应用的未来研究方向和算法框架的观点。

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