数学科学学院学术报告[2025] 028号

(高水平大学建设系列报告1051号)

报告题目：Bayesian Dictionary Learning on Robust Tubal Transformed Tensor Factorization

报告人：骆其伦 特聘研究员（华南师范大学）

报告时间：2025年4月23日上午9：00-11：00

报告形式：腾讯会议（924 752 485）

报告内容：The recent study on tensor singular value decomposition (t-SVD) that performs the Fourier transform on the tubes of a third-order tensor has gained promising performance on multi-dimensional data recovery problems. However, such a fixed transformation, e.g., discrete Fourier transform and discrete cosine transform, lacks being self-adapted to the change of different datasets, and thus it is not flexible enough to exploit the low-rank and sparse property of the variety of multi-dimensional datasets. In this paper, we consider a tube as an atom of a third-order tensor and construct a data-driven learning dictionary from the observed noisy data along the tubes of the given tensor. Then a Bayesian dictionary learning model with tensor tubal transformed factorization, aiming to identify the underlying low-tubal-rank structure of the tensor effectively via the data-adaptive dictionary, is developed to solve the tensor robust principal component analysis problem (TRPCA).  With the defined page-wise tensor operators, a variational Bayesian dictionary learning algorithm is established and updates the posterior distributions instantaneously along the third dimension to solve the TPRCA. Extensive experiments on real-world applications, such as color image and hyperspectral image denoising and background/foreground separation problems demonstrate both effectiveness and efficiency of the proposed approach in terms of various standard metrics.

报告人简介：骆其伦，分别于2015年和2018年在华南师范大学获学士学位和硕士学位，并于2022年在美国伊利诺伊州南伊利诺伊大学卡本代尔分校获数学博士学位。目前是华南师范大学特聘研究员，主要研究方向为数值代数、张量分解与应用、图像处理。学术成果在IEEE TNNLS、IEEE TC、 IEEE TSP、 ACM TIST、Pattern Recognit.、SIAM J. Imaging Sci等多个学术刊物上发表。主持国家自然科学基金青年项目与广东省自然科学基金面上项目各一项。

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邀请人：孙晓丽

数学科学学院

2025年4月22日