Coherent Frame Analysis of Synthetic Aperture Radar (sar) Ocean Imagery.

This Dissertation describes the decomposition and reconstruction of SAR ocean image azimuth cuts using coherent frame theory. The motivation for this work arose from the need to develop new and alternate techniques to approach speckle reduction and feature identification or extraction. Since the ocean is a non-stationary process, the simultaneous time-frequency or space-wavenumber localization characteristics are considerably important. The two dimensional space described by time and frequency or space and wavenumber is called phase space. The methods described provide optimum phase space localization in the sense that they meet the lower limit of the uncertainty principle. To realize optimum phase space localization, the decomposition and reconstruction requires the use of functions that are based on the Gaussian function. Using functions with infinite support on the decomposition process produces non-orthogonal (coupled) coherent states which present serious numerical difficulties for the reconstruction process. To overcome these difficulties, coherent frames are used with oversampling to represent both the Weyl-Heisenberg and the Affine or Wavelet coherent states. The successful reconstruction requires the numerical evaluation and use of the corresponding "dual" frame. The tools are first exercised on a collection of "familiar" waveforms, and are shown to provide unique phase space signatures which illustrate the time (spatial) evolution of a waveform's frequency (wavenumber) content with both types of coherent frames. The tools are then exercised on two different SAR ocean image azimuth cuts. The effects of performing filtering based on the phase space signatures of the SAR ocean image cuts are investigated and demonstrated to extract dominant waveform features. Based on theoretical considerations, a new type of multilevel waveform representation is presented and demonstrated to optimize either the rate of power recovery or minimization of mean square error during the reconstruction process. This new type of filtering technique is a waveform approximation based on using the waveform's coherent states according to magnitude, and is very robust and efficient at recovering dominant waveform features.