【浙江理工大学】An Open Problem on Sparse Representations in Unions of Bases

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

报 告 人：沈益 教授 （浙江理工大学）

报告时间：2024年07月2日（星期二）    上午 10:00-11:30

报告地点：数学科学学院114（小报告厅）

校内联系人：徐敏 副教授            联系电话：84708354

报告摘要：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.

报告人简介：沈益，浙江理工大学数学科学系教授，博导，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）；从事应用调和分析、信息论、逼近论等相关领域的研究；曾主持国家级人才项目，国家自然科学基金面上项目、浙江省杰出青年基金项目等省部级项目；在Appl Comput Harmon A、IEEE T Inform Theory、IEEE T Signal Proces、J Approx Theory、J Fourier Anal Appl、Comput Aided Geom D、J Complexity等期刊发表SCI论文20余篇。