11月15日 沈益教授学术报告

发布时间:2022-11-14

报告题目： An Open Problem on Sparse Representations in Unions of Bases

主讲人：沈益教授，浙江理工大学数学科学系

报告时间：2022/11/15 10:00-11:30

报告地点： 腾讯会议932-684-670（密码：2022）

主持人：李洽副教授

摘要：

We consider sparse representations of signals from redundant dictionaries which are unions ofseveral orthonormal bases. The spark introduced by Donoho and Elad plays an important role in sparserepresentations. However numerical computations of sparks are generally combinatorial. For union:of several orthonormal bases, twolower bounds on the spark via the mutual coherence wereestablished in previous work. We constructively prove that both of them are tiaht Our main result:give positive answers to Gribonval and Nielsen's open problem on sparserepresentations in unions oforthonormal bases. Constructive proofs rely on a family of mutual unbiased bases which first appear:in guantum information theory, lt is joint work with Prof, Song Li, Dr, Yuan Shen and Chenyun Yu.

主讲人简介：

       沈益，浙江理工大学数学科学系教授，浙江省应用数学研究会副理事长，毕业于浙江大学数学系获应用数学博士学位（导师：李松教授），曾获加拿大 Pacific lnstitute for the Mathematical Sciences 资助，于2012至2014期间在加拿大 Alberta 大学（合作导师：韩斌教授）和加拿大 Calgary 大学（合作导师：Elena Braverman教授）从事博士后研究工作。从事应用调和分析，逼近论，信息论等交叉领域的研究。主持国家自然科学基金优秀青年科学基金项目，浙江省杰出青年科学基金项目等省部级项目。在Applied and Computational Harmonic Analysis、IEEE Transaction on lnformation Theory和IEEE Transactions on Signal Processing等期刊发表SCI论文20余篇。