The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color artifacts in deblurring process. To solve this challenging problem, we present a novel cross-space total variation (CSTV) regularization model for color image deblurring by introducing a quaternion blur operator and a cross-color space regularization functional. The existence and uniqueness of the solution are proved and a new L-curve method is proposed to find a balance of regularization terms on different color spaces. The Euler-Lagrange equation is derived to show that CSTV has taken into account the coupling of all color channels and the local smoothing within each color channel. A quaternion operator splitting method is firstly proposed to enhance the ability of color artifacts reduction of the CSTV regularization model. This strategy also applies to the well-known color deblurring models. Numerical experiments on color image databases illustrate the efficiency and effectiveness of the new model and algorithms. The color images restored by them successfully maintain the color and spatial information and are of higher quality in terms of PSNR, SSIM, MSE and CIEde2000 than the restorations of the-state-of-the-art methods.

翻译：彩色图像处理中的跨通道去模糊问题因彩色像素的复杂耦合与结构模糊而难以解决。迄今为止，能够有效减少去模糊过程中彩色伪影的高效算法仍较为有限。为攻克这一难题，本文通过引入四元数模糊算子与跨色彩空间正则化泛函，提出了一种新颖的彩色图像去模糊跨空间全变分正则化模型。我们证明了该模型解的存在性与唯一性，并提出一种新的L曲线方法以实现不同色彩空间正则化项的平衡。通过推导欧拉-拉格朗日方程，证明了该模型同时考虑了所有色彩通道间的耦合关系及各通道内部的局部平滑特性。本文首次提出四元数算子分裂方法以增强跨空间全变分正则化模型的彩色伪影抑制能力，该策略同样适用于现有主流彩色去模糊模型。在彩色图像数据库上的数值实验验证了新模型与算法的效率及有效性。经其复原的彩色图像能完整保持色彩与空间信息，在PSNR、SSIM、MSE及CIEDE2000等指标上均优于现有最先进方法的复原结果。