11月30日 王超助理教授学术报告

发布时间:2023-11-30

报告题目：Scale-invariant regularizations for sparse signal and low-rank tensor recovery

主讲人：王超助理教授，南方科技大学

报告时间：2023/11/30 14:00-17:00

报告地点：腾讯会议452-163-334

主持人：李洽副教授

摘要：

Regularization plays a pivotal role in tackling challenging ill-posed problems by guiding solutions towards desired properties. In this presentation, I will introduce the ratio of the L1 and L2 norms, denoted as L1/L2, which serves as a scale-invariant and parameter-free regularization method for approximating the elusive L0 norm. Our theoretical analysis reveals a strong null space property (sNSP) and proves that any sparse vector qualifies as a local minimizer of the L1/L2 model when a system matrix adheres to the sNSP condition. Furthermore, we extend the L1/L2 model to the realm of low-rank tensor recovery by introducing a tensor nuclear norm over the Frobenius norm (TNF). We demonstrate that local optimality can be assured under an NSP-type condition. Given that both the L1 and L2 norms are absolutely one-homogeneous functions, we propose a gradient descent flow method to minimize the quotient model similarly to the Rayleigh quotient minimization problem. This derivation offers valuable numerical insights into convergence analysis and the boundedness of solutions. Throughout the presentation, we will explore a range of applications, including limited angle CT reconstruction and video background modeling, showcasing the superior performance of our approach compared to state-of-the-art methods.

主讲人简介：

Dr. Wang is an Assistant Professor of the Department of Statistics and Data Science at Southern University of Science and Technology. His research directions are mainly image processing, scientific computing, and interdisciplinary data science, and he has made some innovative contributions to theoretical and algorithmic advances regarding sparsity. In recent years, he has published papers in top journals and academic conferences such as TIP, SISC, SIIMS, ICML, IP, etc. Dr. Wang received the best paper awards in both the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) workshop in 2022 and the 15th China Society of Industrial and Applied Mathematics (CSIAM) Annual Conference in 2017,  as well as obtained the SIAM Student/Early Career Travel Grant Award twice in 2018 and 2020, respectively. Dr. Wang's research is partially supported by the Natural Science Foundation of China (NSFC) Youth Science grant, the Shenzhen Overseas High-level Talents grant (Peacock Project), the Hong Kong Research Grants Council grant, and the Natural Science Foundation of Shenzhen.