20 To 50 percent of the neonates with a very low birth weight (VLBW:< 1500 g) suffer from White Matter Damage (leukomalacia). Nowadays the diagnosis of WMD is still solely dependent on the visual interpretation by an expert. A need for a (semi-) computerized way of segmenting the affected regions, in order to make quantitative measurements as an aid to the subjective diagnosis, is felt. Applying active contours for this purpose, is a classical approach. The performance of active contours for this purpose, however, is heavily deteriorated by the presence of speckle noise. In this paper a new filter, taking into account local statistics in the image, is proposed; it removes a significant amount of speckle noise in the healthy parts, while it makes the areas affected by WMD more uniform, thus severely improving the performance of the active contour. The results show that applying an active contour after the proposed technique yields a segmentation much closer to that of an expert.