题目: New Continuous Representation for Multi-Dimensional Data Recovery Beyond Meshgrid
报告人：赵熙乐 教授（电子科技大学数学科学学院）
邀请人：白敏茹
时间：2023年12月14日 上午11：00-12：00
地点：数学院425
摘要：
Classical low-rank tensor representations can only represent data on meshgrid, which hinders their potential applicability in many scenarios beyond meshgrid. To break this barrier, we propose a low-rank tensor function representation (LRTFR), which can continuously represent data beyond meshgrid with infinite resolution. Specifically, the suggested tensor function, which maps an arbitrary coordinate to the corresponding value, can continuously represent data in an infinite real space. Parallel to discrete tensors, we develop two fundamental concepts for tensor functions, i.e., the tensor function rank and low-rank tensor function factorization. We theoretically justify that both low-rank and smooth regularizations are harmoniously unified in the LRTFR, which leads to high effectiveness and efficiency for data continuous representation. Extensive multi-dimensional data recovery applications arising from image processing (image inpainting and denoising), machine learning (hyperparameter optimization), and computer graphics (point cloud upsampling) substantiate the superiority and versatility of our method as compared with state-of-the-art methods. Especially, the experiments beyond the original meshgrid resolution (hyperparameter optimization) or even beyond meshgrid (point cloud upsampling) validate the favorable performances of our method for continuous representation.
专家简介:
赵熙乐，电子科技大学教授、博士生导师，中国工业与应用数学学会副秘书长，入选电子科技大学百人计划和四川省学术和技术带头人后备人选。撰写Elsevier出版社和科学出版社出版的学术专著章节2章，以第一或通讯作者在高水平期刊和会议发表学术论文60余篇，包括应用数学权威SIAM 系列期刊和图像处理权威IEEE系列期刊(TIP、TNNLS、TCYB、TCI和TGRS)及人工智能权威会议CVPR和AAAI等。主持国家自然科学基金面上项目和青年项目、四川省应用基础研究项目等。研究成果获四川省科技进步奖一等奖(自然科学类、科技进步类)、中国计算数学学会青年优秀论文竞赛二等奖、第一、第二届连续两届川渝科技学术大会优秀论文一等奖、首届四川省数学会应用数学奖二等奖。
