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.

中文翻译：

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用于恢复彩色视频和图像的低秩四元数张量完成

本文提出了一种低秩四元数张量补全方法，一种恢复彩色视频和图像的新方法。我们通过对四元数的三个虚部上的红色、绿色和蓝色通道像素值进行编码，分别将彩色图像和彩色视频重建为四元数矩阵（二阶张量）和三阶四元数张量。不同于一些传统模型将颜色像素作为标量单独表示颜色通道，而在基于四元数的重建过程中，重要的是能够完整地保留彩色图像和彩色视频的固有颜色结构。在 Tucker 秩的定义下，四元数张量之前的全局低秩被编码为展开四元数矩阵的核范数。然后，通过应用 ADMM 框架，我们提供了任意阶四元数张量的张量补全算法，理论上可以很好地用于恢复任何具有颜色结构的多维数据的缺失条目。彩色视频和彩色图像恢复的模拟结果表明，与一些最先进的现有方法相比，所提出的方法具有优越的性能和效率。