SIAM Journal on Imaging Sciences, Volume 14, Issue 1, Page 178-197, January 2021.
Color image restoration is one of the important tasks in color image processing. Covariant differentiation has been applied to handle vector bundles arising from color images in the red, green, blue (RGB) color space. However, there are strong correlations among these three channels, and color image regularization in RGB color space may not be effective enough. The main aim of this paper is to study vector bundles of color images in saturation-value color space and to develop color image regularization models based on vector bundles in saturation-value color space. We develop the saturation-value metric of a vector bundle of $\mathbb{R}^5$-valued functions, and we generalize the vectorial total variation and the vector bundle-valued total variation in saturation-value color space based on the saturation-value metric via the transformation between RGB color space and saturation-value color space. We then develop a saturation-value total variation regularization on vector bundles. We study color image restoration models by using such total variation, and show numerical examples that the proposed color image restoration model outperforms existing methods in terms of visual quality, peak signal-to-noise ratio, and structural similarity.

中文翻译：

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通过矢量束上的饱和度值总变化正则化恢复彩色图像

SIAM影像科学杂志，第14卷，第1期，第178-197页，2021年1月。
彩色图像恢复是彩色图像处理中的重要任务之一。协变微分已应用于处理由红色，绿色，蓝色（RGB）颜色空间中的彩色图像引起的矢量束。但是，这三个通道之间具有很强的相关性，并且RGB颜色空间中的彩色图像正则化可能不够有效。本文的主要目的是研究饱和度值色彩空间中彩色图像的矢量束，并开发基于饱和度值色彩空间中矢量束的彩色图像正则化模型。我们开发了$ \ mathbb {R} ^ 5 $值函数的矢量束的饱和度度量，然后，我们通过RGB色彩空间和饱和度值色彩空间之间的转换，基于饱和度值度量来概括饱和度值色彩空间中的矢量总变化和矢量束值总变化。然后，我们在向量束上开发饱和度值总变化正则化。我们利用这样的总变化研究彩色图像恢复模型，并给出了数值示例，表明所提出的彩色图像恢复模型在视觉质量，峰值信噪比和结构相似性方面均优于现有方法。