Theoretical aspects of Bayesian approach to aperture synthesis for radar imaging

The theory of radar and synthetic aperture radar (SAR) imaging using the maximum likelihood (ML) approach and statistical regularization formalism does not consider two crucial points which are of a prime importance for the statistical optimization of SAR imaging techniques. These are: (1) how to ground the statistical randomized model of the SAR imaging experiment incorporating the maximum entropy principle of information theory; (2) how to design the statistically optimal Bayesian maximum a posteriori probability (MAP) estimation method for solving the inverse problem of restoration of the spatial spectrum pattern (SSP) of the wave field scattered from the probing surface (referred to as the radar image) via processing the finite number of sampled recordings of the SAR trajectory data signals. We fill these gaps by addressing a novel look at the SAR imaging as an ill-conditioned SSP estimation problem with model uncertainties. We extend the theory (see Kravchenko, V.F. et al., Measurement Techniques, vol.58, no.1, p.101-7, 1995) by developing the Bayes ME method for SAR image formation. Our study is intended to establish a foundation to assist in understanding the basic theoretical aspects in designing the signal processing techniques for SAR imagery with enhanced image performance.