学术报告与学术会议

李世东老师受邀进行讲座

发布时间: 2019-12-26 14:37:00

题 目:Enhancing sparsity selections through tail shrinkage and energy relocation

报告人:李世东   教授   San Francisco State University

时 间:2019-12-26 16:30--17:30

地 点:学院401

报告人简介:

       李世东教授从1996至今就职于美国San Francisco State University的数学系。科研方向包括:框架理论及其应用、稀疏信号处理理论及其应用。李教授的博士论文首创了框架多尺度分析理论(Frame Multiresolution Analysis),他亦率先在世界上刻划了框架分解的最一般的形式,并推导了偶框架的一般表达式。李教授还提出并构造了多窗型Gabor分解理论(multi-Gabor expansions)以便多频信号分析的自适应性及改善时频信号分析的分辨率。李教授二十多年里连续荣获美国NSF基金,也同时持有美国空军研究办公室的关于压缩感知的科研项目且拥有多个专利。

摘 要:

       A group of sparsity enhancing techniques through tail shrinkage and tail energy relocations will be presented.  Among others, the focus will be on thresholding algorithms with (tail) feedbacks and null space tuning (NST+HT+FB) and the group of tail shrinkage techniques. The core NST+HT+FB algorithm is shown to converge in finitely many steps. Convergence proofs of variations of the NST + HT+FB mechanisms are also obtained. Necessary and sufficient conditions for unique solution of the tail shrinkage formulation, as well as the error bound analysis will be provided. In addition, a measure theoretical uniqueness of the sparsest solution is established when the sparsity spark(A)/2 < s < spark(A), which is known for having no unique solution in linear algebra. Extensive numerical studies are carried out to demonstrate that these techniques possess substantially superior efficiency over majority (if not all) state-of-the-art sparse selection algorithms at the same level of accuracy.