Quaternion Nuclear Norm minus Frobenius Norm Minimization for Color Image Reconstruction
数学专题报告
报告题目(Title)：Quaternion Nuclear Norm minus Frobenius Norm Minimization for Color Image Reconstruction
报告人(Speaker)：金其余（内蒙古大学）
地点(Place)：后主楼1223 & 腾讯会议：433-787-470
时间(Time)：2024年8月15日 15:00-16:00
邀请人(Inviter)：王发强
报告摘要
Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates quaternion low-rank matrices, resulting in more accurate color image estimation. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.
主讲人简介
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，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。
