Simplified Versions of a Local Wiener Filter

Abstract

Several methods for noise reduction in digital images have been proposed. Classical (global) Wiener filtering is based on the noise power-spectrum and on the expected power spectrum of an ensemble of full images. Sometimes, when such an ensemble is not available one tries to use an ensemble of subimages to be filtered instead. In both cases the filtering cannot adequately deal with localized features. Generalized Wiener filtering has overcome this problem for the situation that such features, like object-background transitions, systematically occur at roughly the same position in all images of the ensemble (PRA). This may be true in some special applications, but even then the method is very complicated. While all these Wiener methods are based on the statistical expectation of global (full-image) parameters, recently filtering methods have been proposed and implemented (KUW, KNU, BER) that use the properties of single-realization local power spectra for space-variant steering of a convolution. These methods work if large local power values are unlikely to be largely due to noise. They can be classified by the following characteristics:

• 1. one or more weighting functions defining spatial windows

• 2. basis functions defining the power analysis (e.g. frequency cells)

• 3. steering functions governing the convolution; and optionally:

• 4. prefab filter functions from which the convolution may be constructed In this paper we present some novel choices of these parameters.