CIF: Small: Adaptive Spectral Estimation and Error Bounding

光谱估计是一种隐身技术，在不同的应用领域中都有广泛的应用。频谱估计在民用和军用的许多应用中起着至关重要的作用。加强理论基础和谱估计算法的质量和鲁棒性，可以发现使用传统方法无法实现的信息获取新技术。这项研究的结果可以为广泛的研究提供新的机会，从建立信号处理逆问题的基础到设计实际适用和可靠的频谱估计算法。本研究利用了压缩感知的最新进展，旨在解决与大规模光谱估计算法开发相关的潜在技术挑战。此外，对现有方法和新方法的不确定性量化和误差范围评估也很重要。度量需要很好地定义，自然是任何定量科学理论的关键要素。本研究旨在推进新型数据自适应频谱估计算法设计的基础知识，并应用数学和工程原理来解决误差边界问题，同时通过以下目标在多个方面推进数学和工程知识：1)数据自适应高分辨率光谱估计方法的发展；2)大规模问题算法的计算效率实现；3)通过在合适的度量中推导误差界限来对方法进行理论定量评估；4)方法在各种现实问题中的应用。

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.