具有非凸与非局部正则化的张量鲁棒主成分分析
Tensor Robust PCA with Nonconvex and Nonlocal Regularization
AI总结：
本文针对TRPCA对奇异值同等收缩及全局低秩假设在视觉数据中受限的问题，提出基于张量可调对数范数的非凸TRPCA，并结合非局部自相似性构建NN-TRPCA模型，通过分组张量增强低秩性，实验证明其在视觉数据恢复上优于现有TRPCA方法。
摘要：
张量鲁棒主成分分析（TRPCA）是一种经典的低秩张量恢复方法，它通过对每个张量奇异值进行同等收缩来最小化张量秩的凸替代。然而，对于真实世界的视觉数据，大奇异值比小奇异值代表更重要的信息。本文提出了一种基于张量可调对数范数的非凸TRPCA（N-TRPCA）模型。与TRPCA不同，我们的N-TRPCA能够自适应地对小奇异值收缩更多，对大奇异值收缩更少。此外，TRPCA假设整个数据张量是低秩的。对于自然视觉数据，这一假设在实践中很难满足，限制了TRPCA从噪声图像和视频中恢复边缘和纹理细节的能力。为此，我们将非局部自相似性集成到N-TRPCA中，进一步提出了非凸非局部TRPCA（NN-TRPCA）模型。具体而言，相似的非局部图像块被分组为一个张量，然后每个分组张量通过我们的N-TRPCA进行恢复。由于同一组中的图像块高度相关，所有分组张量都具有很强的低秩特性，从而提升了恢复性能。实验结果表明，所提出的NN-TRPCA在视觉数据恢复方面优于现有的TRPCA方法。演示代码可在 https://github.com/qguo2010/NN-TRPCA 获取。
英文摘要：
Tensor robust principal component analysis (TRPCA) is a classical way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular value equally. However, for real-world visual data, large singular values represent more significant information than small singular values. In this paper, we propose a nonconvex TRPCA (N-TRPCA) model based on the tensor adjustable logarithmic norm. Unlike TRPCA, our N-TRPCA can adaptively shrink small singular values more and shrink large singular values less. In addition, TRPCA assumes that the whole data tensor is of low rank. This assumption is hardly satisfied in practice for natural visual data, restricting the capability of TRPCA to recover the edges and texture details from noisy images and videos. To this end, we integrate nonlocal self-similarity into N-TRPCA, and further develop a nonconvex and nonlocal TRPCA (NN-TRPCA) model. Specifically, similar nonlocal patches are grouped as a tensor and then each group tensor is recovered by our N-TRPCA. Since the patches in one group are highly correlated, all group tensors have strong low-rank property, leading to an improvement of recovery performance. Experimental results demonstrate that the proposed NN-TRPCA outperforms existing TRPCA methods in visual data recovery. The demo code is available at https://github.com/qguo2010/NN-TRPCA.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
