Color Image Restoration by Saturation-Value Total Variation Regularization on Vector Bundles

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.