Discrete thresholded neural networks of the Hopfield type have been employed to recover the regularized least-squares (LS) solution from noisy image data. The goal is to attain this solution efficiently by conserving computational and storage requirements as the dimensions of the problem grow large. This paper discusses configurations of these networks that recover the LS solution by partitioning the networks and adopting a switching operation between active and inactive partitions to optimize the objective function. Sequential and parallel update procedures on active partitions offer a means to avoid limit cycling and imposing zero-self-feedback constraints. Examples of image noise reduction and the identification of the LS solution from corrupted image data are presented.