数学与统计学院学术报告[2020] 054号

(高水平大学建设系列报告407号)

报告题目: The Tail-null-space-property and the Stability of the Tail-minimization Approach in Compressed Sensing with or without Frames

报告人：李世东  教授（美国旧金山州立大学）

报告时间：2020年7月29日上午10:00—11:00

直播平台及链接： 腾讯会议（会议ID：764 606 460）

报告内容：The $\ell_1$ tail-minimization approach to compressed sensing is seen in an earlier report to be substantially more effective than that of the standard basis pursuit. A measure theoretical uniqueness of the sparsest solution was established when sparsity $m/2 < s < m$, where $m$ is the spark of the sensing matrix $A$.　 A necessary and sufficient condition, tail null space property (tail-NSP), is further established ensuring the unique solution of the $\ell_1$ tail-minimization problem.  The tail-NSP offers an insight about the advantage of the tail-minimization approach over the standard basis-pursuit when a reasonable initial estimate of the support index set $T$ is provided.  A necessary and sufficient tail dictionary NSP (tail-DNSP) has also been established offering the mathematical guarantee of the unique recovery of the associated tail-min sparse frame recovery problem.  Stability results (recovery error bounds) are also obtained in general cases of noisy measurements.  Tail-minimization approach applied to joint sparsity MMV model and theoretical analysis have also a set of extraordinary results.

报告人简历：李世东教授于1993年在美国University of Maryland, Graduate School Baltimore获应用数学博士学位。1993-1994年，李教授就职于美国常青藤联校之一的Dartmouth College，任客座(助)教授，并与1994-1996年就职于University of Maryland, College Park，任客座(助)教授。1996至今，李教授就职于美国San Francisco State University的数学系, 并于2000年获终身(tenured) 教职, 2005 年升任终身正教授。

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　　　　　　　　 　　　　　　　　　　　　　　 2020年7月29日