Academic Report of School of Mathematical Sciences [2026] No. 094

(Series Report for High-Level University Construction No. 1353)

Title：Randomized preconditioned hard thresholding pursuit for sparse approximation

Speaker：Professor Bai Zhengjian(Xiamen University)

Time：10:30-11:30, Oct. 13, 2026

Location：Room 601, Huiyan Building, Yuehai Campus, Shenzhen University

Abstract: Sparsity models with L0-norm constraint are widely used in image processing, statistical regression, wireless communications, and other fields, where numerous thresholding-based methods are employed. However, when the acquisition of linear measurement is time-consuming or the measurement matrix is too large to store in memory, many thresholding-based methods that require the whole measurement matrix become impractical. To address this issue, in this talk, we propose a randomized preconditioned hard thresholding pursuit algorithm for finding a sparse solution to a linear system of equations with L0-norm constraint. The proposed method is also applicable to general settings. It is well-known that Gaussian random matrices satisfy the restricted isometry property (RIP) with high probability, where the RIP of the measurement matrix is crucial for a thresholding-based algorithm to recover a true sparse solution effectively. Taking Gaussian measurement matrices as an illustrative example, we quantitatively analyze how the preconditioner affects the RIP of the measurement submatrix chosen uniformly at random. The linear convergence of the proposed method is also established under some assumptions. Finally, numerical examples based on synthetic and real-world data demonstrate the efficiency of the proposed method.

Speaker Profile：Bai Zhengjian is a professor and doctoral advisor at Xiamen University, a recipient of the Ministry of Education’s New Century Excellent Talents Support Program, and a recipient of the Fujian Province Outstanding Youth Fund. He received his Ph.D. from The Chinese University of Hong Kong in 2004 and has served as a postdoctoral researcher and visiting scholar at the National University of Singapore and the University of Insubria in Italy. His primary research interests include numerical algebra, eigenvalue problems and their inverse problems, sparse optimization, mixed-precision algorithms, optimization algorithms on matrix manifolds, and their applications in data science. He has led general projects funded by the National Natural Science Foundation of China and the Fujian Provincial Natural Science Foundation. He has published numerous academic papers in leading journals in his field, including the SIAM series, Numer. Math., Inverse Problems, Math. Comp., and J. Sci. Comput. He has received the Second Prize of the Fujian Provincial Science and Technology Award.

Faculty and students are welcome to attend!

Invited by: Qu Zheng

School of Mathematical Sciences

October 5, 2026