论文标题
Quaternion Tensor完成，稀疏性颜色视频恢复
Quaternion Tensor Completion with Sparseness for Color Video Recovery
论文作者
论文摘要
本文提出了一种基于四张张量的新型低级完成算法。这种方法使用四元张量的TQT量表在整个过程中维持RGB通道的结构。更详细地，将每个帧中的像素编码在四季度的三个假想部分中，作为四元素矩阵中的元素。然后将每个四元基质堆叠到四元张量中。为了促进张量的低排名，采用对数函数和截短的核定标准来表征四个量张量的等级。此外，通过引入新定义的Quaternion张量离散余弦变换（QTDCT）正则化到低级别近似框架，可以在颜色视频的本地详细信息中获得优化的恢复结果。特别是，四量张量的稀疏性以qDCT结构域中的L1标准为特征。该策略是通过乘数（ADMM）框架的两步交替方向方法优化的。恢复颜色视频的数值实验结果表明，与其他潜在竞争方法相比，该方法的明显优势。
A novel low-rank completion algorithm based on the quaternion tensor is proposed in this paper. This approach uses the TQt-rank of quaternion tensor to maintain the structure of RGB channels throughout the entire process. In more detail, the pixels in each frame are encoded on three imaginary parts of a quaternion as an element in a quaternion matrix. Each quaternion matrix is then stacked into a quaternion tensor. A logarithmic function and truncated nuclear norm are employed to characterize the rank of the quaternion tensor in order to promote the low rankness of the tensor. Moreover, by introducing a newly defined quaternion tensor discrete cosine transform-based (QTDCT) regularization to the low-rank approximation framework, the optimized recovery results can be obtained in the local details of color videos. In particular, the sparsity of the quaternion tensor is reasonably characterized by l1 norm in the QDCT domain. This strategy is optimized via the two-step alternating direction method of multipliers (ADMM) framework. Numerical experimental results for recovering color videos show the obvious advantage of the proposed method over other potential competing approaches.
