Bayesian Inference for Inversion in Synthetic Aperture Imaging Radiometry

Abstract

The inverse problem of synthetic aperture imaging radiometers (SAIRs) has been demonstrated to be not well posed. The regularization methods are crucial for providing unique and stable solutions in the reconstruction of radiometric brightness temperature (BT) maps. Different to deterministic ones, a new approach is presented by referring to the rule of Bayesian inference, providing a probability model of regularized constraints to combat the ill-posedness of finite-dimensional discrete inverse problems. In addition, the SAIR inverse problem can be converted into the probability estimation of the reconstructed BT. Furthermore, in application to both uniformly and nonuniformly spaced arrays, our method can obtain the optimal solution adaptively and avoid the dilemma of choosing the optimal regularization parameter. Finally, simulation results illustrating the effectiveness and performance of the proposed method are provided.