学术讲座【The Multi-Symplectic Lanczos Algorithm and Its Applications to Color Image Processing】
时间：2019年11月23日 (星期六) 09:00 ~ 10:30
地点：旗山校区理工北楼601报告厅
主讲：江苏师范大学教授，贾志刚
主办：数学与信息学院, 福建省分析数学及应用重点实验室
参加对象：感兴趣的老师和学生
报告人简介：贾志刚，江苏师范大学教授。2009年毕业于华东师范大学数学系，获理学博士学位。主要研究方向为数值代数与图像处理，至今已在SIAM J. Matrix Anal. Appl.，SIAM J. Imaging Sci.，J. Sci. Comput.，Numer. Linear Algebra Appl. 等国际知名期刊上发表学术论文30余篇，出版译著1部、教材1部，主持国家自然科学基金项目2项、省部级科研项目1项，参加国家和省自然科学项目4项。先后入选江苏师范大学“第一批高层次人才队伍后备人选”、“三育人先进个人”、“校先进工作者”等。曾经到英国曼彻斯特大学、香港浸会大学等高校数学系进行为期一年的访问。现兼职为中国高等教育学会教育数学专业委员会团体理事、江苏省工业与应用数学会理事、江苏省计算数学学会理事、美国SIAM正式会员、美国Math Review评论员以及SIMAX、Inverse Problem、Automatic等学术期刊的审稿人
报告摘要：The low-rank approximations of original samples are playing more and more important role in many recently proposed mathematical models from the data science. A natural and initial requirement is that these representations inherit original structures or properties. With this aim, we propose a new multi-symplectic method based on the Lanzcos bidiagonalization to compute the partial singular triplets of multi-symmetric matrices. These singular triplets can be used to reconstruct an optimal low-rank approximations with preserving the intrinsic multi-symmetry. The augmented Ritz and harmonic Ritz vectors are used to perform implicit restart to obtain a satisfactory bidiagonal matrix for calculating the k largest or smallest singular triplets, respectively. The newly proposed multi-symplectic Lanczos algorithms are applied to the color image processing, including in the color face recognition and color video compression and reconstruction. Numerical experiments indicate their superiority over the state-of-the-art algorithms.
