Identification and restoration using parallel Kalman filters

In this paper a parallel identification and restoration procedure is described for images with symmetric, noncausal blurs. It is shown that the identification problem can be specified as a parallel set of one-dimensional complex autoregressive moving-average (ARMA) identification problems. By expressing the ARMA models as equivalent infinite-order autoregressive (AR) models, an entirely linear estimation procedure can be followed. It will be shown that under the condition of blur symmetry, it is possible to reconstruct a useful noncausal set of MA (blur) parameters from the identified minimum-phase set. The thus identified image model and blur parameters are supplied to a parallel Kalman restoration filter. Several identification and restoration results on image data are given as examples.