应兰州大学数学与统计学院李朋副教授邀请, 重庆师范大学副教授黄建文, 将于1月26号(星期一)上午9:00-10:00线上举办学术报告。

报告题目: Performance Analysis of Unconstrained Lp Minimization for Sparse Recovery

腾讯会议：794-412-689

报告时间：1月26号(星期一)上午9:00-10:00

报告摘要：In view of coherence, this talk firstly presents a coherence-based theoretical guarantee, including a sufficient condition and associated error estimate, for a non-convex unconstrained Lp (0<p<1) minimization to robustly reconstruct any non-sparse signal in the noisy situation. In a sense, this result supplements the preceding founded ones for the constrained Lp minimization. Specially, when p=1 our coherence-based condition reduces to the state-of-art sharp one. It should also be emphasized that for sparse metric models, based on the theory of coherence, our condition has reached consistency with the corresponding constraint situation. According to the established result, the error in the case that the representative constrained Lp minimization is substituted with unconstrained Lp minimization is also studied. Additionally, the relationship between coherence and null space property (NSP) is discussed and the derived result claims that coherence could imply NSP. In view of the induced NSP, the recovery theory that guarantees the sparse signal can be recovered via the unconstrained Lp minimization is established. Based on the synthetic signals and the real-life signals, it is demonstrated by experimental results that compared with state-of-art methods and convex L1 minimization, the performance of non-convex Lp minimization is more competitive.

报告人简介

黄建文, 重庆师范大学数学科学学院副教授, 硕士生导师。他于2018年在西南大学取得博士学位， 当前主要研究方向为：压缩传感、低秩矩阵恢复、稀疏建模等。主持完成国家自然科学基金1项, 主持在研重庆市自然科学基金面上项目、重庆市教委科技基金青年项目各1项。已在国内外重要刊物, 如IEEE Trans. Neural. Netw. Learn. Syst.、Appl. Comput. Harmon. Anal.、Signal Process.、J. Comput. Math.、Signal Process. Lett.等发表多篇学术论文, 担任多个国际期刊审稿人。详情见其主页https://math.cqnu.edu.cn/info/1234/9398.htm.

肃省计算数学基础学科研究中心

数学与统计学院

萃英学院

2026年1月24日