In this work, we intend to fill the existing methodological-level gaps in the theory of the imaging radar (IR) for remote sensing (RS) systems by addressing a novel look at the RS imaging as an ill-conditioned inverse problem with model uncertainties. We extend the theory presented in the previous studies by developing the fused Bayesian-regularization method for RS image formation subject to the projection-type regularization constraints imposed on the solution. Next, we propose to employ the neural network-based processing for efficient implementation of the developed radar image enhancing algorithms and include some simulation examples to illustrate the overall performances of the proposed approach. Our study is intended to establish the foundation to assist in understanding the basic theoretical aspects fo the multi-level (Bayesian-regularization-neural-network-computing) optimization of the signal processing techniques for enhancing the RS imagery.