Professor Yi Shen was invited to give a lecture

发布时间: 2023-12-20 21:08:00

Topic： An Open Problem on Sparse Representations in Unions of Bases

Speaker：Weizhu Bao

Time：2023-12-15 15:00-16:00

Tencent Meeting ID： 656-4902-4546

Introduction：

    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..

Organizer

School of Mathematical Sciences, South China Normal University, Machine Learning and Optimization Computing Laboratory

Co-organizers

Guangdong Young Scientists Association

Guangdong Computational Mathematical Society