勷勤数学•专家报告

题      目：The springback penalty for robust signal recovery

报  告  人： 安聪沛 教授  (邀请人：王晓宙)

                                    贵州大学

时      间： 5月19日  09：00-10:00

地     点：数科院东楼401

报告人简介:

        安聪沛，贵州大学一流学科特聘教授。本科、硕士毕业于中南大学，师从向淑晃，2011年博士毕业于香港理工大学，师从陈小君(AMS Fellow, SIAM Fellow )和Ian H.Sloan (AMSFellow, SIAM Fellow, Fellow ofthe Australian Academy of Science)。他先后工作于暨南大学和西南财经大学，主持过三项国家自然科学基金，入选四川省“天府峨眉计划”，2023年获得四川省数学会应用数学一等奖，其研究兴趣主要集中在球面设计、振荡积分的近似计算、多项式构造逼近、反问题计算等，研究成果发表在ACHA、SIAM系列杂志、Inverse Problem等期刊上，并取得不少同行的关注，例如2022年菲尔兹奖得主Maryna Vyazovska就曾证明过安聪沛与合作者提出的关于球面设计猜想。

摘      要：

       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.

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