论文标题
更改检测：功能分析的观点
Change Detection: A functional analysis perspective
论文作者
论文摘要
我们开发了一种基于张量的产品表示（例如Karhunen-Loève扩展）来检测随机过程和随机场行为的变化的新方法。从协方差运算符的相关特征空间中，构建了一系列嵌套函数空间，从而可以检测位于正交子空间中的信号。特别是，即使信号的随机行为在全球或局部意义上变化也可以成功。开发了一种数学方法，以基于多层嵌套子空间的构建来定位和测量外部组件的大小。我们在$ \ mathbb {r} $和球形域$ \ mathbb {s}^{2} $中显示了示例。但是，该方法是灵活的，可以在包括时空结构域在内的一般拓扑上检测正交信号。
We develop a new approach for detecting changes in the behavior of stochastic processes and random fields based on tensor product representations such as the Karhunen-Loève expansion. From the associated eigenspaces of the covariance operator a series of nested function spaces are constructed, allowing detection of signals lying in orthogonal subspaces. In particular this can succeed even if the stochastic behavior of the signal changes either in a global or local sense. A mathematical approach is developed to locate and measure sizes of extraneous components based on construction of multilevel nested subspaces. We show examples in $\mathbb{R}$ and on a spherical domain $\mathbb{S}^{2}$. However, the method is flexible, allowing the detection of orthogonal signals on general topologies, including spatio-temporal domains.
