Digital signal restoration using fuzzy sets

A new signal restoration method with considerable flexibility in incorporating a priori information is developed. The method defines a fuzzy set for each piece of information to restrict the set of acceptable solutions. Using fuzzy sets makes it possible to model partially defined information as well as exact knowledge. The intersection of all the fuzzy sets is the feasibility set. The original signal is a member of this set with a high membership value, and any high membership valued element of this set is a nonrejectable solution. Such solutions can be computed by using optimization techniques. Ideally, the feasibility set contains only the original signal. The chance of recovering the original signal decreases as the feasibility set gets larger. Thus, the size of the feasibility set gives a quality measure for the solution. The method generated successful results in many restorations for which the conventional techniques have failed, and may be applied in image coding and tomography.