Regularization Theory In Image Restoration: The Regularizing Operator Approach

This paper presents the application of the regularizing operator (RO) approach in discrete image restoration. This is accomplished by extending the applicability of the RO approach to discrete inverse problems. The concept of the RO is initially presented, and the necessary condition for any operator to be considered as an RO is proposed. On the basis of this condition, a complete mathematical framework for the formation of specific ROs is developed. It is then shown that several operators already known in the literature, including those based on constrained least squares and parametric projection filters, can be considered as special applications of the concept of the RO. On the basis of a new optimality criterion introduced for image restoration, a new class of ROs is then proposed. Several computational issues related to the implementation of an image restoration system are then considered. Under certain assumptions regarding the image formation process, a number of exact regularizing algorithms are proposed. Finally, experimental results are presented, compared, and discussed.