The Family of Regularized Parametric Projection Filters for Digital Image Restoration

Hideyuki IMAI  Akira TANAKA  Masaaki MIYAKOSHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.3   pp.527-534
Publication Date: 1999/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Image Theory
family of projection filters,  family of parametric projection filters,  regularization theory,  

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Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum filter belonging to the family of Projection Filters and Parametric Projection Filters, it is shown that small deviations in the degradation operator and the covariance matrix can cause a large deviation in a restored image. In this paper, we propose new optimum filters based on the regularization method called the family of Regularized Projection Filters, and show that they are stable to deviations in operators. Moreover, some numerical examples follow to confirm that our description is valid.