Statistical Problems in Detectability

点击翻译按钮获取中文摘要

The PI will study statistical problems in detectability, which is to answer whether a detection problem is solvable for a given data set (e.g., an imagery). There will be two major components: (a) what is the fundamental threshold to determine when a detection task is doable, and (b) when a detection problem is solvable, what is the adequate order of computational complexity to solve it. Based on the current state-of-the-art, the PI proposes to derive more accurate results, and to compare different formulations and their influence on the theory of detectability. The proposed works have three main thrusts. (1) Limit distributions of the test statistics at the asymptotic rate of detectability will be derived. This will advancethe detectability theory. (2) Application-driven models will be adopted in the detectability theory. In many cases, these application-driven models are complex, and the adaptation and the possible generalization of the detectability theory are not trivial. (3) Influences of different statistical formulations on the theory of detectability will be characterized. The proposed works are rooted in two of PI's prior works: (1) the project of multiscale geometric detection (MGD), which derived the asymptotic rate of detectability for detecting a range of geometric objects, and (2) the project of multiscale significance run algorithms (MSRA) and theconsequent results on limit distributions. In the second project, after knowing the asymptotic rate in MSRA, the limit distribution of the test statistic is derive (in a simpler situation), so that the detectability right at the asymptotic rate is characterized. The limit distribution also explains the robustness of the detectionalgorithm that have been demonstrated in simulations.Detection is a fundamental problem in many image processing applications. Some applications include (1) particle detection in cryo-EM images, which plays an important role in automated reconstruction of a molecular structure, (2) automatic target recognition (ATR), which has many military and civil surveillance applications, and (3) crater detection in geomorphology, which is utilized in extraterrestrial mapping and planetary chronological research. Proposed theoretical problems are fundamental in theseapplications. Graduate students will get involved.