Medical imaging often requires a preprocessing step where filters are applied that remove noise while preserving semantically important structures such as edges. This may help to simplify subsequent tasks such as segmentation. One class of recent adaptive denoising methods consists of methods based on nonlinear partial differential equations (PDEs). In the present paper we survey our recent results on PDE-based preprocessing methods that may be applied to medical imaging problems. We focus on nonlinear diffusion filters and variational restoration methods. We explain the basic ideas, sketch some algorithmic aspects, illustrate the concepts by applying them to medical images such as mammograms, computerized tomography (CT), and magnetic resonance (MR) images. In particular we show the use of these filters as preprocessing steps for segmentation algorithms.
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