报告人：Professor Qiyu Sun (Department of Mathematics,University of Central Florida,Orlando, FL 32816）
题目: Nonlinear frames and sparse reconstructions
摘要：In this talk, i will consider nonlinear frame theory and sparse reconstruction in Banach space setting.
In this first part of my talk, i will provide some elementary necessary and sufficient conditions for nonlinear maps between Banach spaces to have bi-Lipschitz property, and i will introduce a stable iterative reconstruction algorithm for bi-Lipschitz maps having certain localization property.
In the second part of my talk, i will consider the exponential convergence of the iterative hard thresholding algorithm
to reconstruct sparse signals in a union of closed linear subspaces of a Hilbert space from their nonlinear observations. I will also introduce an optimization framework called sparse approximation triple (SAT), and show that the minimizer in the Banach space could recover the sparse signal in a union of closed linear subspaces of a Hilbert space when the measurement
is almost linear on and has the sparse approximation property.
联系人： 李松 教授