报告人：任欢 博士
报告题目：Quaternion matrix completion with total variation regularization utilizing fast dual proximal gradient method
报告时间：2025年12月6日（周六）下午4：00
报告地点：云龙校区6号楼304会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
任欢，博士，讲师，硕士生导师。主要从事数值代数、数值优化、数据科学等领域的研究，在低秩逼近、矩阵及张量恢复、图像科学、非线性矩阵方程、互补问题的数值求解算法方面有较为深入的研究，且取得了一定的成果。目前主要研究方向为矩阵及张量恢复问题及其在图像处理中的应用。迄今为止主持国家自然科学基金项目1项、江西省自然科学基金项目1项、江西省职业早期青年科技人才培养项目1项。近年来以第一作者在J. Sci. Comput., Calcolo, Numer. Algor., Comput. Math. Appl., Comput. Appl. Math.等国际权威期刊上发表多篇论文。目前担任了Appl. Math. Lett., Comput. Math. Appl., Comput. Appl. Math., Filomat等国际知名期刊审稿人。
报告摘要：
Quaternion matrix completion aims to recover the original image from incomplete image data which has attracted attention in the fields of image and signal processing recently. Unlike traditional algorithms that only consider low-rankness of recovered image, We propose a novel algorithm that combines the Geman function and anisotropic or isotropic total variation (TV) regularization. In the process of solving the model by Alternating direction method of multipliers (ADMM) algorithm, we also employ the fast dual proximal gradient method to address the corresponding sub-problem about the TV regularization. The numerical results on color images demonstrate the effectiveness and reliability of the proposed algorithm.