Generalizations of the non‐linear ocean‐SAR transform and a simplified SAR inversion algorithm

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Abstract
It is demonstrated that the non‐linear transform from the ocean wave spectrum to the synthetic aperture radar (SAR) image spectrum may be extended to include point target spreading (dispersive) effects. For practical purposes, the extension amounts to an additional azimuth spectral cut‐off factor applied to the result of the velocity bunching nonlinear transform without point‐target dispersion. The validity of a quasi‐linear approximation is analysed by means of simple Gaussian test spectra, which also reveal the nature of the fully non‐linear velocity bunching transform. The inversion problem is formulated as a constrained functional minimization over non‐negative wave spectra. An iterative solution method that requires an a priori estimate of the wave spectrum is demonstrated. Analysis of the method leads to a simple theory for preparing the necessary weight functions for the observed SAR and the a priori wave spectra. Combined with an optimized quasi‐linear ocean‐SAR transform, the new formulation leads to a very simple and efficient SAR inversion.