论文标题
基于季化的双线性因子矩阵量标准最小化颜色图像介入
Quaternion-based bilinear factor matrix norm minimization for color image inpainting
论文作者
论文摘要
作为一种新的颜色图像表示工具，Quaternion在颜色图像处理中取得了出色的效果，因为它将颜色图像作为整体而不是单独的颜色空间组件处理，因此它可以充分利用RGB通道之间的高相关性。最近，被证明对颜色图像插入非常有用。在本文中，我们提出了三种基于三个基于四元素的双线性因子（QBF）矩阵最小化模型的新型LRQMC方法。具体而言，我们定义了Quaternion Double Frobenius Norm（Q-DFN），Quaternion双核标准（Q-DNN）和Quaternion frobenius/nuc Norm（Q-FNN），然后显示它们与基于Quaternion的矩阵Schatten-P（Q-Schatten-P）的关系。所提出的方法可以避免用于大型四元素矩阵的四元素奇异值分解（QSVD），因此与现有（LRQMC）方法相比，可以有效地减少计算时间。实验结果表明，所提出的方法的性能优于某些最先进的低级别（四元）矩阵完成方法。
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.
