江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Hypergraph regularized and low-rank enhanced tucker decomposition for image restoration
报告人：卢琳璋 教授 单位：厦门大学、贵州师范大学
报告时间：2025年12月6日（周六）上午9:00--10:00
报告地点：数学学院A321
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数学学院
报告人简介：
卢琳璋，博士，二级教授、博士研究生导师。现任国际学术期刊“Numerical Algebra, Control and Optimization” (数值代数，控制及优化) 编委。
主要学术成就:
在国内外著名学术刊物上已发表学术论文160多篇, 其中包括发表在SIAM SCI. COMPUT.，SIAM MATRIX ANA. APPL.，NUMER. MATH.，PATTERN RECOGN., EXPERT SYS. APPL., NEURAL NETWORKS 等国际著名学术刊物上的SCI论文110多篇。一些论文的成果已分别被写入中外著名学者撰写的四本（包括2本SIAM出版社出版的）专著。
主持完成国家自然科学基金项目6项，作为主要合作者参加国家自然科学基金重点项目1项，国家自然科学基金项目4项。主持，参加省自然科学基金项目多项，获得过国家攀登计划青年基金，国家留学回国基金和科技部973计划项目基金。现正主持一项国家自然科学基金项目。
个人的研究项目在2001年获得了省科技进步奖，与学生合作的2个研究项目分别在2016年，2019年获得了省自然科学奖。
教书育人：
在厦门大学和贵州师范大学从教30多年，已培养了近40名博士（包括一名来自巴基斯坦的博士生，7名和国外导师联合培养的博士生），40多名硕士。现正在指导培养的博士生还有5位。
主要研究领域:
数值分析, 数值代数, 矩阵/张量分析和计算，数据科学。
Abstract: Image restoration, aiming to reconstruct the original image from its degraded version, is a crucial problem in image processing. Tucker decomposition is one of the prominent tool in image restoration for high-dimensional tensor data. The prior knowledge of images, including global correlation and local similarity structures, is often combined with tensor decomposition to tackle image restoration issues. Deeply exploring and effectively utilizing these prior knowledge has become the key to improving the performance of image restoration techniques. In terms of local similarity, most of the work that has achieved good recovery capability revolves around graphbased manifold regularization. However, hyper-graph can better cover the geometric structure of the original tensor than simple graph. To simultaneously consider the global low rankness and local similarity of inherent image features, hyper-graph regularization and sparsity are jointly embedded in a low-rank approximation manner. The paper proposes a novel hypergraph regularized and low-rank enhanced Tucker decomposition (called HGLRTD) for image restoration. A easily implementable algorithm and the closed -form updating rules are designed to solve the HGLRTD model. Numerical experiment results demonstrate that the proposed method outperforms many state-of-the-art tensor completion methods in terms of quality metrics and visual effects.