Noise Filtering and Testing for MR Using a Multi-Dimensional Partial Volume Model

One of the most common problems in image analysis is the estimation and removal of noise or other artefacts (e.g., grey level quantization) using spatial filters. Common tech-niques include Gaussian Filtering, Median Filtering and Anisotropic Filtering. Though these techniques are quite common in the image processing literature they must be used with great care on medical data, as it is very easy to introduce artifact into images due to spatial smoothing. The use of such techniques is further restricted by the absence of gold standard data against which to test the behaviour of the filters. Following a general dis-cussion of the equivalence of filtering techniques to likelihood based estimation using an assumed model, this paper describes an approach to noise filtering in multi-dimensional data using a partial volume data density model. The resulting data sets can then be taken as gold standard data for spatial filtering techniques which use the information from sin-gle images. We explain how such data has advantages over data generated purely by simulation when testing alternative algorithms.