论文标题
基于双变量等效的最小值concave惩罚的低级张量完成
Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penalty
论文作者
论文摘要
低量张量完成（LRTC）是计算机视觉和机器学习中的重要问题。 Minimax-concave惩罚（MCP）作为非凸宽松的功能在LRTC问题中取得了良好的结果。要使MCP的所有恒定参数作为变量函数，以便提高对LRTC问题中奇异值变化的适应性，我们提出了双变量等效的minimax-concave惩罚（BEMCP）定理。将BEMCP定理应用于张量奇异值会导致双变量加权张量$γ$ -Norm（BEWTGN）定理，我们分析和讨论其相应的特性。此外，为了促进LRTC问题的解决方案，我们给出了BEMCP定理和BEWTGN的近端操作员。同时，我们为LRTC问题提出了一个BEMCP模型，该模型是根据交替方向乘数（ADMM）最佳解决的。最后，提出的方法应用于现实世界中多光谱图像（MSI），磁共振成像（MRI）和彩色视频（CV）的数据还原，实验结果表明，它表现出优于最先进的方法。
Low-rank tensor completion (LRTC) is an important problem in computer vision and machine learning. The minimax-concave penalty (MCP) function as a non-convex relaxation has achieved good results in the LRTC problem. To makes all the constant parameters of the MCP function as variables so that futherly improving the adaptability to the change of singular values in the LRTC problem, we propose the bivariate equivalent minimax-concave penalty (BEMCP) theorem. Applying the BEMCP theorem to tensor singular values leads to the bivariate equivalent weighted tensor $Γ$-norm (BEWTGN) theorem, and we analyze and discuss its corresponding properties. Besides, to facilitate the solution of the LRTC problem, we give the proximal operators of the BEMCP theorem and BEWTGN. Meanwhile, we propose a BEMCP model for the LRTC problem, which is optimally solved based on alternating direction multiplier (ADMM). Finally, the proposed method is applied to the data restorations of multispectral image (MSI), magnetic resonance imaging (MRI) and color video (CV) in real-world, and the experimental results demonstrate that it outperforms the state-of-arts methods.
