Tensor Recovery via L-Spectral k-Support Norm
Tensor Recovery via L-Spectral k-Support Norm
复制标题
通过 L 谱 k 支持范数恢复张量
DOI：
10.1109/jstsp.2021.3058763
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发表时间：
2021
影响因子：
7.5
通讯作者：
Qibin Zhao
中科院分区：
文献类型：
--
作者：
Andong Wang;Guoxu Zhou;Zhong Jin;Qibin Zhao
与对原始域中的低秩进行建模的传统张量分解不同，最近提出的张量奇异值分解（-SVD）通过利用谱域中的低秩为张量分析带来了新的曙光。对于–SVD 框架内的凸秩最小化，张量–Tubal Nuclear Norm (–TNN) 在许多应用中优于矩阵核范数的经典张量扩展。在本文中，我们首先将 TNN 推广到谱支持范数（-SpSN-）作为一种新的低秩正则化器，然后采用它来制定两个估计器，用于从噪声线性观测中恢复张量。此外，通过建立估计误差的确定性和非渐近上限来分析所提出的估计器的统计性能，这表明所提出的张量 Dantzig 选择器在张量压缩感知和张量完成方面具有接近最优的估计误差。此外，导出了所提出的范数的近端算子并将其嵌入到有效的算法中来计算估计量。合成数据集上的实验验证了所提出的误差范围的正确性，图像修复结果证明了所提出的估计器的优越性。
Unlike traditional tensor decompositions which model low-rankness in the original domain, the recently proposed tensor-Singular Value Decomposition (–SVD) casts a new light on tensor analysis by exploiting low-rankness in the spectral domain. For convexized rank minimization within the framework of–SVD, the tensor–Tubal Nuclear Norm (–TNN) outperforms classical tensorial extensions of matrix nuclear norm in many applications. In this paper, we first generalize–TNN to the-Spectral-Support Norm (-SpSN-) as a new low-rank regularizer, and then adopt it to formulate two estimators for tensor recovery from noisy linear observations. Further, statistical performance of the proposed estimators is analyzed by establishing both deterministic and non-asymptotic upper bounds on the estimation error, which indicates that the proposed tensor Dantzig selector enjoys near-optimal estimation error for tensor compressive sensing and tensor completion. Moreover, proximal operator of the proposed norm is derived and embeded in an efficient algorithm to compute the estimators. Experiments on synthetic datasets verify correctness of the proposed error bounds and image inpainting results demonstrate superiority of the proposed estimators.