CIF: Small: Adaptive Spectral Estimation and Error Bounding

University Of Florida, Gainesville FL

Investigators

Abstract

This research focuses on the development of data-adaptive algorithms and error bounds for spectral estimation, which is a stealth technology in diverse application fields. Spectral estimation plays a critical role in many applications, civil as well as military. Strengthening the theoretical underpinnings and the quality and robustness of spectral estimation algorithms enables the discovery of new technologies for information acquisition which would not have been possible using traditional methods. The results of this study can provide new opportunities in a wide range of studies ranging from building on the fundamentals of inverse problems for signal processing to devising practically applicable and reliable spectral estimation algorithms. This research leverages the recent advances in compressive sensing and is aimed at addressing the underlying technical challenges associated with the development of large scale spectral estimation algorithms. Moreover, quantifying uncertainty and assessing error bounds for current and new methods is also of significant importance. A metric needs to be well defined and naturally is a key element in any quantitative scientific theory. This research seeks to advance fundamental knowledge in novel data-adaptive spectral estimation algorithm design and to apply mathematical and engineering principles to address error bounding, while advancing mathematical and engineering knowledge on multiple fronts through the objectives listed below: 1) development of data-adaptive high resolution spectral estimation methods, 2) computationally efficient implementations of the algorithms for large scale problems, 3) theoretical quantitative assessment of the methods by deriving error bounds in suitable metrics, and 4) application of the methods to diverse real-world problems.