The standard formulation of the Wiener filter has met limited success in image processing because of its lowpass characteristics, which give rise to unacceptable blurring of lines and edges. If the signal is a realization of a non-Gaussian process such as in natural images, the Wiener filter is outperformed by nonlinear estimators. One reason why the Wiener filter blurs the image significantly is that a fixed filter is used throughout the entire image, the filter is space invariant.
A number of attempts to overcome this problem have adopted a nonstationary approach where the characteristics of the signal and the noise are allowed to change spatially [10-23].
The Wiener filter in Eq. (30) defines a shift-invariant filter, and thus the same filter is used throughout the image. One way to make the filter spatially variant is by using a local spatially varying model of the noise parameter an. Such a filter can be written as
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