Constrained Kalman filtering for image restoration

The author considers the incorporation of deterministic a priori signal information in the Kalman filtering of images. This information, in the form of constraints, is used to achieve `ringing´ reduction by adaptive regularization of the restoration filter. The signal constraints are first transformed into constraints on the Kalman gain. Constrained optimization of the Kalman gain is then implemented using a penalty function approach. The constraints considered are bounds on signal amplitude and signal local variance. The proposed scheme provides a hybrid image restoration that minimizes the mean square error subject to the given a priori constraints. A simple but effective heuristic Kalman algorithm, which uses a `tuning´ parameter to achieve ringing reduction, is proposed