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Image restoration step is important in many image processing applications. In this work, we attempt to restore radiological images degraded during acquisition and processing. Details of the work, carried out to optimize a Neural Network (NN) for identifying an AutoRegressive Moving Average (ARMA) model used for nonlinearly degraded image restoration, are presented in this paper. The degraded image is expressed as an ARMA process. To improve the learning performance, the NN is fast trained using a hybrid swarm intelligence optimization approach based on the synergy of Particle Swarm (PSO) and Bacterial Foraging (BFO) Algorithms, which is compared with other training techniques such as: The back propagation, Quasi-Newton and Levenberg-Marquardt Algorithms. Both original image and blur function are identified through this model. The optimized ARMA-NN model is implemented on a Xilinx reconfigurable Field-Programmable Gate Array (FPGA) using hardware description language: VHDL. This VHDL code is tested on the rapid prototyping platform named ML505 based on a Virtex5-LXT FPGA chip of Xilinx. Simulation results using some test and real images are presented to support the applicability of this approach compared to the standard blind deconvolution method that maximizes the likelihood using an iterative process. The comparison is based on performance evaluation using some recent image quality metrics.