The springback penalty for robust signal recovery

Time: 2026-05-19 21:11:00

Title: The springback penalty for robust signal recovery
Speaker: Professor An Congpei (Invited by Wang Xiaozhou)
Affiliation: Guizhou University
Time: May 19, 09:00–10:00
Venue: Room 401, East Building of the School of Mathematical Sciences

Speaker Biography:
    An Congpei is a specially appointed professor of the first-class disciplines at Guizhou University. He received his bachelor's and master's degrees from Central South University under the supervision of Xiang Shuhuang, and earned his Ph.D. in 2011 from The Hong Kong Polytechnic University under the co-supervision of Chen Xiaojun (AMS Fellow, SIAM Fellow) and Ian H. Sloan (AMS Fellow, SIAM Fellow, Fellow of the Australian Academy of Science). He has previously worked at Jinan University and Southwestern University of Finance and Economics. He has served as principal investigator for three projects of the National Natural Science Foundation of China, was selected for the "Tianfu Emei Plan" of Sichuan Province, and won the First Prize in Applied Mathematics from the Sichuan Mathematical Society in 2023. His research interests mainly focus on spherical designs, approximate computation of oscillatory integrals, polynomial construction and approximation, and inverse problems. His work has been published in journals such as Applied and Computational Harmonic Analysis (ACHA), SIAM journals, and Inverse Problems, and has attracted considerable attention from the community. For example, Maryna Viazovska, the 2022 Fields Medalist, proved a conjecture on spherical designs proposed by An Congpei and his collaborators.

Abstract:
    We propose a new penalty, the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, the springback penalty is a weakly convex function. It bears various theoretical and computational advantages of both the benchmark convex penalty and many of its non-convex surrogates that have been well studied in the literature. We establish the exact and stable recovery theory for the recovery model using the springback penalty for both sparse and nearly sparse signals, respectively, and derive an easily implementable difference-of-convex algorithm. In particular, we show its theoretical superiority to some existing models with a sharper recovery bound for some scenarios where the level of measurement noise is large or the amount of measurements is limited. We also demonstrate its numerical robustness regardless of the varying coherence of the sensing matrix. The springback penalty is particularly favorable for the scenario where the incomplete and inaccurate measurements are collected by coherence-hidden or -static sensing hardware due to its theoretical guarantee of recovery with severe measurements, computational tractability, and numerical robustness for ill-conditioned sensing matrices.