Professor Qian Tao was invited to give a lecture

发布时间: 2023-03-20 00:54:57

Topic：Sparse Representations in Hilbert Spaces

Speaker: Qian Tao

Time: Tuesday, March 7th, 2023, 3:30-4:30 PM (Beijing time)

Tencent Meeting ID: 669-2471-6718

Introduction:

Motivated by positive frequency decomposition there first speared the so called adaptive Fourier decomposition (AFD) in around 2011. The method is a type of sparse representation of signals in the complex Hardy H2 space by parameterised Szego dictionary elements. Based on delicate complex and harmonic analysis it is a more sophisticated matching pursuit methodology than the general greedy algorithm. AFD then was extended into general Hilbert spaces with a dictionary enjoying boundary vanishing condition (BVC), called pre-orthogonal AFD (POAFD).It then was further generalised to form an Sn$-Best approximation (n-Best)equivalent to best approximation by rational functions of degree not exceeding $n$, and stochastic AFD etc., the latter being comparable with the Karhunen-Lo-eve expansion (Principal Component Analysis) in stochastic analysis. The talk will provide detailed information about the mentioned sparse representations, as well as their applications.

Organizers: South China Normal University, School of Mathematical Sciences, Machine Learning and Optimization Computing Laboratory Co-organizer

Guangdong Young Scientists Association