报告名称：Continuous Representation-Induced Regularization Methods for Multi-Dimensional Data Recovery

报告专家：孟德宇

专家所在单位：西安交通大学

报告时间：2024年10月21日下午3:00-6:00

报告地点: 数统学院201报告厅

专家简介： 孟德宇，西安交通大学教授，博导，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，NSR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。

报告摘要：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- 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.