Partially-blind image restoration using constrained Kalman filtering

A constrained Kalman filtering approach for the restoration of images blurred by random point-spread functions (PSFs) is proposed. The effects of the blur model uncertainties are treated as image-dependent correlated noise, and they require the formulation of an augmented-state Kalman filter. Additional a priori image information, including deterministic information, is incorporated into the augmented-state Kalman filter as convex set constraints. Efficient constrained optimization of the augmented-state Kalman gain is achieved by projecting the unconstrained optimal gain onto the convex sets. The proposed constrained filter is useful in cases of image restoration where the degrading PSF is only partially known, such as in the presence of error in blur model parameters