Prior knowledge regularization in statistical medical image tasks

The estimation of the covariance matrix is a pivotal step in several statistical tasks. In particular, the estimation becomes challenging for high dimensional representations of data when few samples are available. Using the standard Maximum Likelihood estimation (MLE) when the number of samples are lower than the dimension of the data can lead to incorrect estimation e.g. of the covariance matrix and subsequent unreliable results of statistical tasks. This limitation is normally solved by the well-known Tikhonov regularization adding partially an identity matrix; here we discuss a Bayesian approach for regularizing the covariance matrix using prior knowledge. Our method is evaluated for reconstructing and modeling vertebra and cartilage shapes from a lower dimensional representation and a conditional model. For these central problems, the proposed methodology outperforms the traditional MLE method and the Tikhonov regularization.