学术报告

题      目：An Open Problem on Sparse Representations in Unions of Bases

报  告  人：沈益  教授  (邀请人：叶颀 )

                                    浙江理工大学

时      间：12月18日  10：00-11：00

地     点：数科院西楼111报告厅

报告人简介:

        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 Institute 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 Information Theory》和《IEEE Transactions on Signal Processing》等期刊发表SCI论文20余篇。

摘      要：

        We consider sparse representations of signals from redundant dictionaries which are unions of several orthonormal bases. The spark introduced by Donoho and Elad plays an important role in sparse representations. However, numerical computations of  sparks are generally combinatorial. For unions of several orthonormal bases, two lower bounds on the spark via the mutual coherence were established in previous work. We constructively prove that both of them are tight. Our main results give positive answers to Gribonval and Nielsen's open problem on sparse representations in unions of orthonormal bases. Constructive proofs rely on a family of mutual unbiased bases which first appears in quantum information theory.  It is joint work with Prof. Song Li, Dr. Yuan Shen and Chenyun Yu.

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