Open Problems on Sparse Representations in Unions of Bases
2021-12-02 15:00:00
2021-12-02 15:00:00
2021-12-02 15:00:00
Speaker : 3:00PM，Yi Shen
Time : 2021-12-02 15:00:00
Location :
Speaker: Yi Shen (Zhejiang Sci-Tech University)
Date: December 2 Thur. 3:00pm
Venue: Tencent Meeting Room: 951 684 427 Password: 310027
Abstract: 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.