This paper describes a statistical framework for the unsupervised learning of linear filter combinations for feature characterisation. The learning strategy is two step. In the first instance, the EM algorithm is used to learn the foreground probability distribution. This is an abductive process, since we have a detailed model of the background process based on the known noise-response characteristics of the filter-bank. The second phase uses the a posteriori foreground and background probabilities to compute a weighted between-class covariance matrix. We use the principal components analysis to locate the linear filter combinations that maximise the between class covariance matrix. The new feature characterisation method is illustrated for the problem of extracting linear features from complex millimetre radar images. The method proves to be effective in learning a mixture of sine and cosine phase Gabor functions necessary to capture shadowed line structures.