Abstract: Compressed sensing is an active topic recently. In this talk, we will introduce some basic results in compressed sensing. In particular, we will introduce the definition of RIP matrix and the performance of \ell_1 minimization. Moreover, we will show a deterministic method to sample high dimensional Chebyshev polynomial space, for which the possible applications include uncertainty quantification and numerically solving stochastic or parametric PDEs. We prove the recovery performance of the deterministic points by Weil's theorem in number theory. Finally, we use the numerical experiments to show that the deterministic points have a similar performance with that of the random points. The talk is based in part on joint work with Tao Zhou.

 

报告人简介: 许志强, 中科院数学与系统科学研究院副研究员。主要研究方向为逼近论、压缩感知及与之相关的离散数学问题。毕业于大连理工大学, 并于清华大学、德国柏林工业大学做博士后研究。曾获得中科院卢嘉锡青年科学奖, 中科院数学与系统科学研究院“陈景润未来之星”等奖励。研究工作中, 一方面，他将纯粹数学中的一些方法引入计算调和分析, 从而在信号量化、压缩感知、小波等领域一些困难问题取得实质性进展; 另一方面，他将逼近论中样条函数与代数、多面体相结合, 从而解决了多个猜想与公开问题, 并在该方向作了系统与深入的工作。这些研究在几个原本似乎毫无关联的领域之间建立了联系。

 

Date&Time: September 18, 2013 (Wednesday), 14:00 - 15:00
Location: 606 Conference Room