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

• Applicant: Professor Peter Schreier, Ph.D.
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2013 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 239765482

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.

• DFG Programme: Research Grants