The problem of ill conditioning is examined for atmospheric turbulence and diffraction limited spread functions. The results of the restoration of simulated pictures under separable spread functions are presented. In order to solve the ill conditioning of the restoration problem, a priori information in the form of deterministic constraints is proposed. A comparison with existing methods like Wiener filter, smoothing and regularizing techniques is made. Linear equality constraints reduce the variance of the estimators, but some bias may be introduced if the constraints are not valid.
Experimental results show that more acceptable restored pictures are obtained in the restoration.
Linear inequality constraints are incorporated by means of a quadratic programming formulation. The natural constraint of nonnegativeness of pixel values is handled in a formal way, as well as other types of restrictions that can be described by linear inequalities. Experimental results indicate a substantial improvement in the restoration even for the ill conditioned situation.