报告题目 (Title)：A New Cross-Space Total Variation Regularization Model for Color Image Restoration with Quaternion Blur Operator (四元数模糊算子下彩色图像恢复的跨空间全变分正则化模型)

报告人 (Speaker)：贾志刚 教授（江苏师范大学）

报告时间 (Time)：2024年12月15日(周日) 15:00-16:30

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：刘巧华

主办部门：理学院数学系

报告摘要：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 is 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.