论文标题
低排时四元张量完成，用于恢复颜色视频和图像
Low-rank quaternion tensor completion for recovering color videos and images
论文作者
论文摘要
本文提出了低级四元张量张量完成方法，一种新型的恢复颜色视频和图像的方法。我们分别通过编码四个假想部分的红色，绿色和蓝色通道像素值来编码红色，绿色和蓝色通道像素值，分别重建彩色图像和彩色视频为四元素矩阵（二阶张量）和三阶四元基量。与一些传统模型不同，这些模型将颜色像素视为标量并分别表示颜色通道，而在基于季节的重建过程中，很重要的是，可以完全保留颜色图像和彩色视频的固有色结构。在塔克等级的定义下，四量张量之前的全球低级别被编码为展开季节矩阵的核标准。然后，通过应用ADMM框架，我们为任何订单四基张量提供了张量完成算法，从理论上讲，这些算法可以很好地用于恢复带有色结构的任何多维数据的缺失条目。彩色视频和彩色图像恢复的仿真结果表明，所提出的方法的性能和效率优于某些最新的现有方法。
Low-rank quaternion tensor completion method, a novel approach to recovery color videos and images is proposed in this paper. We respectively reconstruct a color image and a color video as a quaternion matrix (second-order tensor) and a third-order quaternion tensor by encoding the red, green, and blue channel pixel values on the three imaginary parts of a quaternion. Different from some traditional models which treat color pixel as a scalar and represent color channels separately, whereas, during the quaternion-based reconstruction, it is significant that the inherent color structures of color images and color videos can be completely preserved. Under the definition of Tucker rank, the global low-rank prior to quaternion tensor is encoded as the nuclear norm of unfolding quaternion matrices. Then, by applying the ADMM framework, we provide the tensor completion algorithm for any order quaternion tensors, which theoretically can be well used to recover missing entries of any multidimensional data with color structures. Simulation results for color videos and color images recovery show the superior performance and efficiency of the proposed method over some state-of-the-art existing ones.
