Luo Yi-Si, Zhao Xi-Le, Jiang Tai-Xiang, Chang Yi, Ng Michael K, Li Chao
IEEE Trans Image Process. 2022;31:3793-3808. doi: 10.1109/TIP.2022.3176220. Epub 2022 Jun 2.
Recently, transform-based tensor nuclear norm (TNN) minimization methods have received increasing attention for recovering third-order tensors in multi-dimensional imaging problems. The main idea of these methods is to perform the linear transform along the third mode of third-order tensors and then minimize the nuclear norm of frontal slices of the transformed tensor. The main aim of this paper is to propose a nonlinear multilayer neural network to learn a nonlinear transform by solely using the observed tensor in a self-supervised manner. The proposed network makes use of the low-rank representation of the transformed tensor and data-fitting between the observed tensor and the reconstructed tensor to learn the nonlinear transform. Extensive experimental results on different data and different tasks including tensor completion, background subtraction, robust tensor completion, and snapshot compressive imaging demonstrate the superior performance of the proposed method over state-of-the-art methods.
最近，基于变换的张量核范数（TNN）最小化方法在多维成像问题中恢复三阶张量方面受到越来越多的关注。这些方法的主要思想是沿三阶张量的第三模式执行线性变换，然后最小化变换后张量的正面切片的核范数。本文的主要目的是提出一种非线性多层神经网络，以自监督的方式仅使用观测张量来学习非线性变换。所提出的网络利用变换后张量的低秩表示以及观测张量与重构张量之间的数据拟合来学习非线性变换。在不同数据和不同任务（包括张量补全、背景减法、鲁棒张量补全和快照压缩成像）上的大量实验结果表明，所提出的方法优于现有方法。
