Nonlinear Sampling Theory: Sparsity, Localization and Optimization

The University Of Central Florida Board Of Trustees, Orlando FL

Investigators

Abstract

Recent technological advances have made it possible to reconsider the idea of distributing spatially a large number of small devices that have actuating, sensing, computing, and telecommunications capabilities. Such spatial implementations can provide unprecedented capabilities for new applications in spatially distributed networks. The investigator explores methods of nonlinear sampling for distributed signal acquisition systems, with attention to engineering applications. This interdisciplinary project has broader impact on mathematical, engineering and industrial problems, ranging from nonlinear frame theory and nonlinear signal processing to smart energy, transportation, and security networks. Students are trained in the course of this project. In this project, the principal investigator develops a novel mathematical framework to analyze and synthesize spatial signals with compressive parametric representations. He develops globally robust algorithms for cases where communication and energy resources are limited. He investigates development of optimal sampling methodologies for analysis and synthesis of smart signal acquisition in engineering networks. The main themes of this project are based on localization techniques in spatial domains, quasi-Banach algebraic relaxations of sparsity measures, and Hilbertization of quasi-optimality in Banach spaces.