An image restoration method that performs piecewise smooth restorations on images corrupted with very high noise levels is presented. The restoration is based on a Markov random field (MRF) model using a neural network sigmoid nonlinearity between pixels to produce a restoration with sharp boundaries while providing noise reduction. The model is currently implemented using an efficient deterministic search algorithm that typically requires less than 200 iterations in a digital computer simulation. The algorithm is able to restore images with up to 71% of the pixels corrupted with sensor noise (non-gaussian). Results from simulation indicate that the MRF restoration is capable of operating at signal-to-noise ratios 5 to 6 dB lower than the median filtering. The same model can be applied to a large number of sensor measurements (Doppler, intensity, passive infrared, range, and video sensors) by simply adjusting a single parameter. This is especially relevant for hardware implementation, since a single chip can be used for processing a wide variety of imagery. The model has a massively parallel architecture with local neighbor interactions (four nearest neighbors), and can be implemented on a large parallel computer or a custom analog VLSI chip. Implementation of the model in analog VLSI would allow video rate restoration of 512 X 512 pixel images.