Statistical Problems in Detectability

PI将研究可检测性中的统计问题，即回答检测问题是否可用于给定的数据集（例如，图像）。将有两个主要组成部分：（a）什么是基本的阈值，以确定何时检测任务是可行的，（B）当一个检测问题是可解决的，什么是适当的计算复杂性的顺序来解决it.Based上的当前国家的最先进的，PI建议，以获得更准确的结果，并比较不同的配方和它们的可检测性理论的影响。拟议的工程有三个主要目标。(1)极限分布的检验统计量的渐近检测率将被推导出来。这将推进可探测性理论。(2)可探测性理论将采用应用驱动模型。在许多情况下，这些应用驱动的模型是复杂的，可检测性理论的适应和可能的推广并不是微不足道的。(3)不同的统计公式的可探测性理论的影响将被表征。所提出的工作是植根于两个PI的先前的作品：（1）项目的多尺度几何检测（MGD），推导出检测范围的几何对象的可检测性的渐近速率，和（2）项目的多尺度显着运行算法（MSRA）和极限分布的对比结果。第二个方案是在已知MSRA的渐近速率后，（在较简单的情况下）得到检验统计量的极限分布，从而刻画了在渐近速率下的可检测性。极限分布也解释了检测算法的鲁棒性，并在仿真中得到了验证。检测是许多图像处理应用中的一个基本问题。一些应用包括（1）低温EM图像中的粒子检测，其在分子结构的自动重建中起重要作用，（2）自动目标识别（ATR），其具有许多军事和民用监视应用，以及（3）地貌学中的陨石坑检测，其用于地外测绘和行星年代学研究。提出的理论问题是这些应用中的基础。研究生将参与其中。

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.