基于四元数的双线性因子矩阵范数最小化彩色图像修复
Quaternion-based bilinear factor matrix norm minimization for color image inpainting
摘要：
四元数作为一种新的彩色图像表示工具，在彩色图像处理中取得了很好的效果，因为它将彩色图像作为一个整体而不是作为一个单独的颜色空间分量来处理，从而可以充分利用RGB通道之间的高度相关性。近年来，低秩四元数矩阵补全（LRQMC）方法被证明是非常有用的彩色图像修复。在本文中，我们提出了三个新的LRQMC方法的基础上三个四元数为基础的双线性因子（QBF）矩阵范数最小化模型。定义了四元数双Frobenius范数（Q-DFN）、四元数双核范数（Q-DNN）和四元数Frobenius/核范数（Q-FNN），并给出了它们与基于四元数的矩阵Schatten-p（Q-Schatten-p）范数的关系。该方法避免了对大型四元数矩阵进行四元数奇异值分解（QSVD）的计算，与现有的LRQMC方法相比，可以有效地减少计算时间.实验结果表明，所提出的方法优于一些国家的最先进的低秩（四元数）矩阵完成方法的性能。
英文摘要：
As a new color image representation tool, quaternion has achieved excellent results in the color image processing, because it treats the color image as a whole rather than as a separate color space component, thus it can make full use of the high correlation among RGB channels. Recently, low-rank quaternion matrix completion (LRQMC) methods have proven very useful for color image inpainting. In this paper, we propose three novel LRQMC methods based on three quaternion-based bilinear factor (QBF) matrix norm minimization models. Specifically, we define quaternion double Frobenius norm (Q-DFN), quaternion double nuclear norm (Q-DNN) and quaternion Frobenius/nuclear norm (Q-FNN), and then show their relationship with quaternion-based matrix Schatten-p (Q- Schatten-p ) norm for certain p values. The proposed methods can avoid computing quaternion singular value decompositions (QSVD) for large quaternion matrices, and thus can effectively reduce the calculation time compared with existing (LRQMC) methods. The experimental results demonstrate the superior performance of the proposed methods over some state-of-the-art low-rank (quaternion) matrix completion methods.
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