The family of regularized parametric projection filters for digital image restoration

Optimum filters for an image restoration are formed by a degradation operat or, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the co variance 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 a nd 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 Filt ers, and show that they are stable to deviations in operators. Moreover, so me numerical examples follow to confirm that our description is valid.