深圳大学数学科学学院

荔园学者Colloquium第九十二期

讲座题目: Continuous Representation-Induced Regularization Methods for Multi-Dimensional Data Recovery

主讲人：孟德宇 教授 （西安交通大学）

讲座时间：2024年8月19日下午16：00-17：00

讲座地点：深圳大学粤海校区汇星楼514

报告内容：Most classical regularization-based methods for multi-dimensional imaging data recovery can solely represent multi-dimensional discrete data on meshgrid, which hinders their potential applicability in many scenarios beyond meshgrid. To break this barrier, we propose a series of continuous functional representation methods, which can continuously represent data beyond meshgrid with powerful representation abilities. Specifically, the suggested continuous representation manner, which maps an arbitrary coordinate to the corresponding value, can continuously represent data in an infinite real space. Such an ameliorated representation regime always facilitates better efficiency, accuracy, and wider range of available domains (e.g., non-meshgrid data) of regularization based methods. In this talk, we will introduce how to revolutionize the conventional low-rank, TV, non-local self-similarity regulation methods into their continuous ameliorations, i.e., Low-Rank Tensor Function Representation (termed as LRTFR), neural domain TV (termed as NeurTV), and Continuous Representation-based NonLocal method (termed as CRNL), respectively. We will also show extensive multi-dimensional data recovery applications arising from image processing (like image inpainting and denoising), machine learning (like hyperparameter optimization), and computer graphics (like point cloud upsampling) to validate the favorable performances of our method for continuous representation.

主讲人简介：孟德宇，西安交通大学教授，博导，国家级领军人才，任大数据算法与分析技术国家工程实验室机器学习教研室负责人。发表论文百余篇，谷歌学术引用超过30000次。现任IEEE Trans. PAMI，Science China: Information Sciences等7个国内外期刊编委。目前主要研究聚焦于元学习、概率机器学习、可解释性神经网络等机器学习基础研究问题。

欢迎师生参加！

邀请人：数学科学学院（鲁坚）

　 数学科学学院

2024年8月17日