Recovering structured signals: atoms, matrix separation, and applications

University Of North Carolina At Wilmington, Wilmington NC

Investigators

Abstract

High dimensional data sensing, representation, and recovery that utilize the data’s intrinsic low dimensionality have become pervasive in many applications, including signal processing, computer vision, and machine learning. This project involves the development and analysis of new solutions for sensing and analyzing high dimensional data, inspired by the electrodermal activity (EDA) signal decomposition problem. A cleaner EDA decomposition allows scientists and data analysts to extract better features to serve a variety of tasks such as market research, seizure detection, human stress analysis, and emotion recognition, leading to social and economical benefits. In particular, this project aims to increase the recovery rate of medication-assisted treatment in rehabilitation centers. Many of the expected results will also be applicable to other imaging modalities as well as machine learning applications. Undergraduate and master students will be mentored as part of this project. The students will also have opportunities to work with peers and researchers to better understand and contribute to real world applications. This project aims to recover structured signals that are intrinsically low dimensional with significantly subsampled measurements. The project involves an analysis of the sensing conditions needed for the subsampled measurements and how they benefit the structured signals expressed in terms of few atoms. A framework for a generalized matrix decomposition will also be developed, which will be suitable for the EDA decomposition setting. Efficient algorithms for solving the associated novel optimization problems will also be developed and implemented. The new framework developed in this project combined with rigorous theoretical guarantees are expected to strengthen existing partnerships with other disciplines such as psychology and industry. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.