Relations between nonlinear filters in digital image processing

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Nonlinear filters are very popular for image restoration, since they allow denoising without deterioration of edges. Although many different methodologies have been developed in parallel, their connections have hardly been studied so far. In this project we intend to examine the relations between three important classes of nonlinear filters, namely local discrete filters, diffusion filters and wavelet techniques. We will analyse these relations not only theoretically but we will also study numerical implementations and perform practical evaluations. In order to derive a unifying description of the three classes, we investigate formulations in terms of unconstrained optimization problems, discrete weighted averaging methods and parabolic partial differential equations (PDEs). We will compare the different techniques both for synthetical images as well as for widely used real-world test images.