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.<
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