CIF: Small: Adaptive Spectral Estimation and Error Bounding

谱估计是一种应用广泛的隐身技术，本文重点研究了谱估计的数据自适应算法和误差界。谱估计在民用和军用的许多应用中都扮演着重要的角色。加强谱估计算法的理论基础以及质量和稳健性，能够发现新的信息获取技术，而这是使用传统方法无法实现的。这项研究的结果可以为广泛的研究提供新的机会，从建立信号处理的逆问题的基本原理到设计实用和可靠的谱估计算法。这项研究利用了压缩传感的最新进展，旨在解决与大规模谱估计算法开发相关的潜在技术挑战。此外，量化不确定度和评估现有方法和新方法的误差范围也具有重要意义。度量需要被很好地定义，并且自然是任何量化科学理论中的关键要素。这项研究旨在提高新型数据自适应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界限问题，同时通过以下目标在多个方面促进数学和工程知识：1)开发数据自适应高分辨率谱估计方法，2)大规模问题的算法的计算高效实现，3)通过在适当的度量中导出误差界对方法进行理论定量评估，以及4)将方法应用于不同的现实世界问题。

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.