Time：9:00am
Date:  November 22, 2019
Venue：Room 338, Nanhai Building
 
Topic 1：Exact Phase-Retrievable Frames
Abstract：An exact phase-retrievable frame $\{f_{i}\}_{i}^{N}$ for an $n$-dimensional Hilbert space is a phase-retrievable frame that fails to be phase-retrievable if anyone element is removed from the frame. Such a frame could have different lengths. We shall prove that for the real Hilbert space case,  exact phase-retrievable frame of length $N$ exists for every $2n-1\leq N\leq n(n+1)/2$. For arbitrary frames  we introduce the concept of redundancy with respect to its phase-retrievability and the concept of frames with exact PR-redundancy.
Speaker：Prof. Sun Wenchang, from Nankai University
 
Topic 2：On a group of tail shrinkage techniques for enhanced sparsity selections
Abstract：A group of sparsity enhancing techniques through tail shrinkage and tail energy relocations will be presented.  Among others, the focus will be on thresholding algorithms with (tail) feedbacks and null space tuning (NST+HT+FB) and a group of tail shrinkage techniques. The core NST+HT+FB algorithm is shown to converge in finitely many steps. Convergence proofs on variations of the NST + HT+FB mechanisms are also obtained. Necessary and sufficient conditions for the unique solution of the tail shrinkage formulation, as well as the error bound analysis will be provided. In addition, a measure theoretical uniqueness of the sparsest solution is established when the sparsity s is in the range of spark(A)/2 < s < spark(A), which is known for having no unique solution in linear algebra. Extensive numerical studies are carried out to demonstrate that these techniques possess substantially superior efficiency over majority state-of-the-art sparse selection algorithms at the same level of accuracy.
Speaker: Prof Li Shidong, from San Francisco State University

Topic 3：Differential Privacy for Sparse Learning Algorithms
Abstract：Differential privacy is a notion of privacy that provides useful information while concealing the individual information. We propose a unify framework differential privacy for sparse regularization algorithms which can applied to the most popular sparse learning algorithms. We show effective and effectual of the framework by applying to the popular machine learning algorithm with differential privacy such as Lasso, SCAD, MCP, L1/2  regularizer.
Speaker：Prof. Zhang Hai, Northwest University

 
Topic 4：An Algorithm for Recovering Bandlimited Graph Signals
Abstract：Signal recovery on graphs is attracting more and more attentions. Based on the smoothness assumption, the signal recovery problem can be formulated as an unconstrained optimization model. To reduce the computational complexity, we construct a kernel function of a reproducing kernel Hilbert space, such that the smoothness item is equivalent to the norm of the signal modulo a constant. Based on this, the optimization problem for recovering the signal from a given bandlimited space can be solved with less computational cost.
Speaker：Prof. Yang Lihua，Sun Yat-sen University