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Projection filter, Wiener filter, and Karhunen-Loève subspaces in digital image restoration. (English) Zbl 0588.94005
In image processing by computer, the transformation from the original continuous-domain image to the degraded and sampled discrete observation image is usually modelled as a linear transformation with additive noise. The relation between two types of filters, the Wiener filter (WF) and the projection filter (PF), for the restoration of the original image from the observation is discussed. The latter is based on the same principle as pseudoinverse filtering but also suppresses the additive noise. The PF and the WF are shown to be closely related under a condition depending on the degradation-sampling operator and the Karhunen-Loève expansion for the family of original images. The relation between the PF and the Gauss- Markov estimator is also clarified.
##### MSC:
 94A99 Communication and information 68T10 Pattern recognition, speech recognition