Properties of different estimates of the regularizing parameter for the least-squares image restoration problem
Nikolas P. Galatsanos, Aggelos K. Katsaggelos · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1991
Image restoration is a necessary step for higher level machine or human image analysis. In many applications image data are blurred and corrupted by additive noise. Because of the presence of singularities in the blurring operator regularization is an effective method for obtaining satisfactory solutions to image restoration problems. The application of regularization necessitates a choice of a regularizing parameter which trades fidelity to the data with smoothness of the restored image. For most problems of interest the choice of the regularizing parameter is not known a priori. Methods based on the properties of the residuals and on the generalized cross-validation have been proposed for estimating the regularizing parameter. In this paper alternative methods are proposed to compute the regularizing parameter. The resulting values of the regularizing parameter are compared with the values resulting from the above mentioned methods. Furthermore it is shown that under certain conditions all the above mentioned methods result in the same value for the regularizing parameter. Experimental results are presented which verify the previous theoretical results. 590 / SPIE Vol. 1396 Applications of Optical Engineering: Proceedings of OE/Midwest ''90