Synthetic Aperture Inversion for Statistically Nonstationary Target and Clutter Scenes

We introduce a class of nonstationary stochastic processes suitable for modeling nonstationary radar targets and clutter. This class of processes can be characterized by pseudodifferential operators driven by the Wiener process. We refer to these processes as pseudostationary processes and define a concept of space-varying spectral density function using the symbol of the underlying operators. We then derive an analytic filtered-backprojection- and backprojection-filtering-type formulas based on the minimum mean square error criterion for synthetic aperture image reconstruction. The inversion formulas depend on the space-varying spectral density function of target and clutter. We present an algorithm for the simultaneous estimation of target a priori information and reconstruction of SAR images. The algorithm is computationally efficient and can be implemented with the computational complexity of fast-backprojection algorithms. Extensive numerical simulations demonstrate the performance of the method.