Gao Quanxue, Zhang Pu, Xia Wei, Xie Deyan, Gao Xinbo, Tao Dacheng
IEEE Trans Pattern Anal Mach Intell. 2021 Jun;43(6):2133-2140. doi: 10.1109/TPAMI.2020.3017672. Epub 2021 May 11.
Despite the promising results, tensor robust principal component analysis (TRPCA), which aims to recover underlying low-rank structure of clean tensor data corrupted with noise/outliers by shrinking all singular values equally, cannot well preserve the salient content of image. The major reason is that, in real applications, there is a salient difference information between all singular values of a tensor image, and the larger singular values are generally associated with some salient parts in the image. Thus, the singular values should be treated differently. Inspired by this observation, we investigate whether there is a better alternative solution when using tensor rank minimization. In this paper, we develop an enhanced TRPCA (ETRPCA) which explicitly considers the salient difference information between singular values of tensor data by the weighted tensor Schatten p-norm minimization, and then propose an efficient algorithm, which has a good convergence, to solve ETRPCA. Extensive experimental results reveal that the proposed method ETRPCA is superior to several state-of-the-art variant RPCA methods in terms of performance.
尽管取得了令人鼓舞的成果，但张量鲁棒主成分分析（TRPCA）旨在通过同等收缩所有奇异值来恢复被噪声/异常值破坏的干净张量数据的潜在低秩结构，却无法很好地保留图像的显著内容。主要原因是，在实际应用中，张量图像的所有奇异值之间存在显著的差异信息，并且较大的奇异值通常与图像中的一些显著部分相关联。因此，应该对奇异值进行不同的处理。受此观察结果的启发，我们研究在使用张量秩最小化时是否存在更好的替代解决方案。在本文中，我们开发了一种增强的TRPCA（ETRPCA），它通过加权张量Schatten p范数最小化明确考虑张量数据奇异值之间的显著差异信息，然后提出一种具有良好收敛性的高效算法来求解ETRPCA。大量实验结果表明，所提出的ETRPCA方法在性能方面优于几种最新的变体RPCA方法。
