The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for tensor completion. The main idea of this type of methods is exploiting the low-rank structure of frontal slices of the targeted tensor under the linear transform along the third mode. However, the low-rankness of frontal slices is not significant under linear transforms family. To better pursue the low-rank approximation, we propose a nonlinear transform-based TNN (NTTNN). More concretely, the proposed nonlinear transform is a composite transform consisting of the linear semi-orthogonal transform along the third mode and the element-wise nonlinear transform on frontal slices of the tensor under the linear semi-orthogonal transform, which are indispensable and complementary in the composite transform to fully exploit the underlying low-rankness. Based on the suggested low-rankness metric, i.e., NTTNN, we propose a low-rank tensor completion (LRTC) model. To tackle the resulting nonlinear and nonconvex optimization model, we elaborately design the proximal alternating minimization (PAM) algorithm and establish the theoretical convergence guarantee of the PAM algorithm. Extensive experimental results on hyperspectral images, multispectral images, and videos show that the our method outperforms linear transform-based state-of-the-art LRTC methods qualitatively and quantitatively.
翻译:以线性变换为基础的高压核规范(TNN)方法最近取得了令人乐观的结果,最终最终将最终完成。这类方法的主要想法是利用第三种模式线性变换中目标粒子在线性变换线性变换线性变换线性变换线性变换线性变换线性变换线性变压前部分的低位结构。然而,在线性变换组合中,前端切子的低位并不是显著的。为了更好地追求低级变换近端,我们建议采用非线性变换TNNNN(NTNNNNN)模式。更具体地说,拟议的非线性变换是一种复合变换,包括沿第三种模式的线性半正态变换线性,以及线性变换线性变换线性色素前部的元素非线性变换形。我们精心设计了线性变异性变异性变异性变异性变异性变异性变异性变异性变异性变异性变异性变异性变异性变异性变异性变异性模型(PAMXMISLMISMLMLMISMLMLMISLMLMMLMLMLMLA) 和制变制变制结果。根据低性变异性变真性变变变变变变后,我们制的理论性变真性变变变变变变变变变制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制式和制制制制制制制制制制制制制制的模型和制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制的模型,以制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制制,我们制制制,我们制制制制制制制制制制式制式制制制制制制