2-D Kalman filtering for the restoration of stochastically blurred images

2D Kalman filtering for the restoration of stochastically blurred images is developed. Stochastic blur is treated as the combination of a deterministic blur and correlated random noise. For restoration from single-frame data, an augmented state-vector Kalman filter for stochastic blurs is derived. This filtering scheme is then extended to provide restoration from multiple-frame data also. Kalman filtering for both serial and parallel processing of the frames is proposed. The new filters can take into account the spatio-temporal correlations of the randomly varying blur. For the equivalent 1-D problem, the proposed filters are the best linear estimators for minimizing the mean-square error over the blur process ensemble and observation noise ensemble. Sample results are also provided to show the effectiveness of the proposed filters