Spectral Analysis of Gapped or Missing Data

缺省或缺省数据的频谱分析这项研究侧重于缺省或不完整数据序列的频谱分析。当很长一段时间的连续数据测量很难获得或某些间隔内的测量由于强干扰或干扰而无效而必须丢弃时，通常会出现间隔或丢失数据的问题。缺失或不完整数据序列的谱分析在天文、通信、医学成像、雷达和水声等领域有着广阔的应用前景。本研究涉及到对不完整数据序列进行高效和稳健的谱分析算法的开发和应用。这项研究的目标是设计和评估各种应用的统计上可靠的和数学上可靠的谱分析方法，这些方法涉及到对有间隙或不完整数据序列的谱分析，获得对算法特性的实践和理论上的见解，包括精度、分辨率、收敛和计算复杂性，并了解大间隙或大量缺失数据样本对算法设计的影响。预计这项研究的结果将对许多实际应用的进展产生重大影响。

Jian LiSpectral Analysis of Gapped or Missing DataThis research focuses on the spectral analysis of gapped or incomplete data sequences. The gapped or missing data problem usually arises when contiguous data measurements for a long time are hard to obtain or the measurements during some intervals are not useful due to strong interference or jamming and must be discarded. Spectral analysis of gapped or incomplete data sequences holds promise to advance many fields including astronomy, communications, medical imaging, radar, and underwater acoustics.This research involves the development and application of efficient and robust spectral analysis algorithms for incomplete data sequences. The goals of this research are to devise and evaluate statistically sound and mathematically solid spectral analysis methods for various applications that involve the spectral analysis of gapped or incomplete data sequences, to gain both practical and theoretical insights into the algorithm properties including accuracy, resolution, convergence, and computational complexity, and to understand the impacts of large gaps or large numbers of missing data samples on the algorithm design. It is anticipated that the results of this study will significantly impact the advances of many practical applications.