Enhancing Sparsity Selections through Tail Shrinkage and Energy Relocation

Time: 2019-12-26 17:15:00

Topic：Enhancing Sparsity Selections through Tail Shrinkage and Energy Relocation

Speaker：Shidong Li       San Francisco State University

Time：2019-12-26 15:00--16：00

Location：Room 305 in School of Mathematical Sciences

Introduction：

     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 the group of tail shrinkage techniques. The core NST+HT+FB algorithm is shown to converge in finitely many steps. Convergence proofs of variations of the NST + HT+FB mechanisms are also obtained. Necessary and sufficient conditions for 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 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 (if not all) state-of-the-art sparse selection algorithms at the same level of accuracy.