School of Mathematical Sciences Academic Report [2025] No. 028  

(High-Level University Construction Series Report No. 1051)  

Lecture Title: Bayesian Dictionary Learning on Robust Tubal Transformed Tensor Factorization

Speaker: Luo Qilun (Distinguished Research Fellow, South China Normal University)  

Date & Time: 9:00–11:00 AM, April 23, 2025  

Format: Tencent Conference (Meeting ID: 924 752 485)  

Abstract: 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.

Biography: Luo Qilun received his B.S. (2015) and M.S. (2018) from South China Normal University and his Ph.D. in Mathematics from Southern Illinois University Carbondale, USA (2022). Currently he is a Distinguished Research Fellow at South China Normal University, his research focuses on numerical algebra, tensor decomposition and applications, and image processing. His publications appear in IEEE TNNLS, IEEE TC, IEEE TSP, ACM TIST, Pattern Recognition, and SIAM J. Imaging Sci. He presides over one National Natural Science Foundation Youth Project and one Guangdong Provincial Natural Science Foundation General Project.  

All faculty and students are welcome to attend!

Invited by: Sun Xiaoli  

School of Mathematical Sciences  

April 22, 2025