Geometric Methods with Application to Robust Detection and Estimation

摘要

We have obtained a number of results pertaining to image compression, robust estimation, and robust signal detection. All of this work has admitted the presence of data whose statistics are imperfectly known. Our results have featured adaptivity, flexibility, and nontraditional approaches. In order to employ more realistic statistical models, we have directed our research to admit nonstationarity and dependency. Much of our work in robust estimation and detection has employed a geometric approach which we have originated in past research. Our geometric techniques provide a quantitive way to measure the degree of robustness, thus offering the designer more flexibility in meeting the performance/robustness needs of the user. Our most recent results have resulted in the admission of essentially arbitrary dependent data, thus leading to a number of important conclusions pertaining to signal detection and the estimation of a random variable. (KR)