Dr. Li Jiao visited Macau University of Science and Technology on June 19, 2026. She was warmly received by Professor Qian Tao, Director of the Macau Centre for Mathematical Sciences of Macau University of Science and Technology, and Associate Professor Xiao Xuanxuan, Assistant Director of the Macau Centre for Mathematical Sciences.
During her visit, Dr. Li Jiao delivered an academic presentation entitled "Theoretical Exploration of Convolution Random Sampling and Reconstruction in Shift-Invariant Spaces," presenting systematic research results on two core mathematical settings.
This work studies convolution random sampling and reconstruction in shift-invariant spaces for two settings. The first setting concerns the Radon transform in two-dimensional computerized tomography. For functions with compact support, we identify admissible direction vectors and random sampling sets. We prove that the sampling inequality holds with high probability when the sample size is sufficiently large. Moreover, every function in a locally multiply generated shift-invariant space is uniquely determined by its convolution Radon random samples, and we derive an explicit reconstruction formula. The second setting concerns convolution sampling with derivatives in multiply generated periodic shift-invariant spaces. We prove that for random sampling sets, the sampling inequality holds with high probability when either the sample size or the decomposition constant is sufficiently large. An explicit stable reconstruction formula is also provided.
From September 2021 to December 2025, Li Jiao pursued her Ph.D. at the School of Mathematics, Sun Yat-sen University, under the supervision of Professor Jun Xian. Since January 2026, she has been a postdoctoral researcher at the School of Mathematics and Statistics, Henan Normal University, working with Professor Guangyue Huang. Her research interests include sampling theory and its applications in signal processing, Radon transform and CT image reconstruction, as well as derivative sampling and signal reconstruction. Related results have been published in journals such as Banach Journal of Mathematical Analysis, Applicable Analysis, and Taiwanese Journal of Mathematics. She has also been invited to serve as a reviewer for IEEE Transactions on Signal Processing.
Photo of Professor Qian (left) and Dr. Li Jiao (right)
