Analysis of the SAR imaging process of the ocean surface using Volterra models

The synthetic aperture radar (SAR) process of the ocean surface mapping is studied using a decomposition based on a Volterra model. By a mathematical expansion of the complex exponential of the complete SAR transform, these models decompose the nonlinear distortion mechanisms of the SAR spectrum over different spectra of polynomial interactions. Thus, they offer an alternative modeling (to the exact SAR transform) giving a theoretical separation between the SAR Fourier components linearly derived from the sea surface elevation and the artifacts created by nonlinearities of the SAR mapping of the ocean surface. The paper gives a systematic assessment of such an approximation of the ocean surface SAR imaging process. Higher order statistics (HOS) of the SAR transform and their calculus and implementation are presented. In fact, nonlinearity detection, location (in the Fourier domain) and quantification can only be performed by HOS, reduced to a second-order Volterra model. The Volterra expansion of the SAR imaging process opens new theoretical inversion schemes since under certain conditions on the linear part, Volterra models are easily invertible. Our method is first tested on simulated SAR images in order to validate the HOS tools. We then show results of this nonlinearity analysis performed on images from the ERS-1 satellite and we present cases of nonlinearity detection.