A Bayesian approach to Fourier Synthesis inverse problem with application in SAR imaging

Abstract. In this paper we propose a Bayesian approach to the ill-posed inverse problem of Fourier synthesis (FS) which consists in reconstructing a function from partial knowledge of its Fourier Transform (FT) with application in SAR (Synthetic Aperture Radar) imaging. The function to be estimated represents an image of the observed scene. Considering this observed scene is mainly composed of point sources, we propose to use a Generalized Gaussian (GG) prior model, and then the Maximum A posterior (MAP) estimator as the desired solution. In particular, we are interested in bi-static case of spotlight-mode SAR data. In a first step, we consider real valued reflectivities but we account for the complex value of the measured data. The relation between the Fourier transform of the measured data and the unknown scene reflectivity is modeled by a 2D spatial FT. The inverse problem becomes then a FS and depending on the geometry of the data acquisition, only the set of locations in the Fourier space are different. We give a detailed modeling of the data acquisition process that we simulated, then apply the proposed method on those synthetic data to measure its performances compared to some other classical methods. Finally, we demonstrate the performance of the method on experimental SAR data obtained in a collaborative work by ONERA1.