讲座人介绍：

金其余，内蒙古大学教授、博导。法国南布列塔尼大学应用数学博士，巴黎六大、上海交通大学博士后，巴黎-萨克雷高等师范学校访问学者，内蒙古自治区“青年科技英才支持计划”青年科技领军人才，中国数学会医学数学专业委员会委员，中国运筹学会数学规划分会理事，内蒙古自治区数学学会理事。长期与国内外多所大学保持合作，包括法国巴黎-萨克雷高等师范学校、巴黎六大、Centre Inria Rennes等。研究领域包括：图像处理、计算机视觉与最优化。相应成果发表于SIAM Journal on Imaging Sciences、Cell子刊Structure、Journal of scientific computing、Journal of Mathematical Imaging and Vision，TIP，PR，Inverse problems等期刊。主持国家自然科学基金、内蒙古自然科学基金等项目多项。

讲座简介：

Color image restoration often suffers from artifacts due to inadequate modeling of inter-channel correlations. To address this, we propose a robust framework that leverages quaternion algebra for holistic color representation. Central to our approach is a novel regularization technique—Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF)—which effectively captures the intrinsic low-rank structure of color images encoded as quaternion matrices. Additionally, we introduce the Quaternion Nuclear Norm over Frobenius Norm (QNOF), a nonconvex, parameter-free surrogate for quaternion matrix rank. QNOF simplifies to a singular value $L_1/L_2$ minimization problem and is integrated into a robust matrix completion framework using the alternating direction multiplier method with theoretical convergence guarantees. Together, QNMF and QNOF enable superior performance across diverse low-level vision tasks such as denoising, deblurring, and inpainting. Extensive experiments demonstrate that our quaternion-based models significantly outperform existing methods, offering a mathematically grounded and efficient solution for color image restoration under challenging conditions.