推广的张量鲁棒主成分分析模型及其应用
Extended Tensor Robust Principal Component Analysis Model and Its Application
DOI: 10.12677/PM.2023.138246, PDF,    国家自然科学基金支持
作者: 王 颖, 唐科威：辽宁师范大学数学学院，辽宁 大连
关键词: 张量；核范数；倾斜图像恢复；高斯噪声；动态背景分割；Tensor； Nuclear Norm； Skewed Image Recovery； Gaussian Noise； Dynamic Background Segmentation
摘要: 近年来，张量在处理可视化数据方面有广泛的应用，以鲁棒主成分分析(RPCA)为基础，将其扩展至张量情况，张量鲁棒主成分分析(TRPCA)被提出，该模型已经成功应用于恢复彩色图像、视频的前背景分割等方面。然而TRPCA仅仅考虑了本身具有低秩性的图像，不能校正倾斜的彩色图像，为了解决这个问题，本文通过考虑变换后张量的低秩性和稀疏性进行建模，对TRPCA进行了推广，同时，我们还引入了张量的F范数来更好地处理高斯噪声和分割视频的动态背景。最后，在不同类型的彩色图像和视频上进行了大量实验，证明了本文方法的有效性。
Abstract: In recent years, tensors have been widely used in processing visualization data. To extend robust principal component analysis (RPCA) to tensor situations, tensor robust principal component analysis (TRPCA) has been proposed, and this model has been successfully applied to color images restoration, video background segmentation, and other aspects. However, TRPCA only considers images with low rank properties and cannot correct skewed color images. To solve this problem, we extend TRPCA by considering the low rankness and sparsity of the transformed tensor. In addition, we also introduce F norm to better handle Gaussian noise and segment the dynamic background of video. Finally, a large number of experiments are conducted on different types of color images and videos to demonstrate the effectiveness of the proposed method.
文章引用：王颖, 唐科威. 推广的张量鲁棒主成分分析模型及其应用[J]. 理论数学, 2023, 13(8): 2378-2387. https://doi.org/10.12677/PM.2023.138246

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