Prior knowledge regularization in statistical medical image tasks
Alessandro Crimi, Jon Sporring, Marleen de Bruijne, Martin Lillholm, Mads Nielsen · Research at the University of Copenhagen (University of Copenhagen) · 2009
The estimation of the covariance matrix is a pivotal step inseveral statistical tasks. In particular, the estimation becomes challeng-ing for high dimensional representations of data when few samples areavailable. Using the standard Maximum Likelihood estimation (MLE)when the number of samples are lower than the dimension of the datacan lead to incorrect estimation e.g. of the covariance matrix and subse-quent unreliable results of statistical tasks. This limitation is normallysolved by the well-known Tikhonov regularization adding partially anidentity matrix; here we discuss a Bayesian approach for regularizing thecovariance matrix using prior knowledge. Our method is evaluated forreconstructing and modeling vertebra and cartilage shapes from a lowerdimensional representation and a conditional model. For these centralproblems, the proposed methodology outperforms the traditional MLEmethod and the Tikhonov regularization.