Nonparametric Techniques for Analyzing Directional Structure in Space-Time Random Fields

分析图像和时空数据中的方向结构对许多应用至关重要，因为一维模式通常对应于物体轮廓或轨迹等重要特征。例如，合成孔径雷达（Synthetic Aperture Radar， SAR）图像经常被用于分析海浪、飓风雨带、海啸等结构，这些结构都表现为局部单向结构。许多现有的方向估计工作处理的是确定性数据；另一方面，关于随机场的大部分工作都集中在各向同性的情况下。在这个项目中，我们建议发展非参数技术来分析随机图像和时空随机场中的方向结构。更具体地说，我们在这项建议中的目标是：1。建立一个空间平稳性测试。这一假设在文献中很常见，但令人惊讶的是，很少有正式的测试。2. 建立对图像中单向结构的测试。由于大多数随机场仅在某些斑块和特定频率范围内显示单向性，因此我们的测试将定位在空间和波数域。从包含多个高度定向分量的图像中识别和提取单向分量。将我们的结果扩展到多维和时空随机场。这种扩展必须考虑到时空场的特殊结构，将时间变量与空间变量分开处理。

The analysis of directional structure in images and space-time data is crucial to many applications since one-dimensional patterns often correspond to important features such as object contours or trajectories. For example, Synthetic Aperture Radar (SAR) images are frequently analyzed for structures such as oceanic waves, hurricane rain bands, tsunamis, etc., which all exhibit locally unidirectional structure. Much of the existing work on orientation estimation treats deterministic data; on the other hand, much of the work on random fields has focused on the isotropic case. In this project, we propose to develop nonparametric techniques for analyzing directional structure in random images and space-time random fields. More specifically, our objectives in this proposal are:1. To build a test for spatial stationarity. This assumption is commonplace in the literature, yet there exist surprisingly few formal tests for it. 2. To build a test for unidirectional structure in images. As most random fields display unidirectionality only in some patches and only in certain frequency ranges, our tests will be localized in the spatial and wavenumber domains.3. To identify and extract unidirectional components from images that contain several highly directional components.4. To extend our results to multidimensional and space-time random fields. Such an extension must take into account the special structure of space-time fields by treating the temporal variable separately from the spatial variables.