Partially discrete magnetic resonance tomography

In Magnetic Resonance (MR) image reconstruction, under-sampled data sets lead to ill-posed reconstruction problems. To regularize these problems, prior knowledge is commonly exploited. In this work, we introduce a new type of prior knowledge, partial discreteness, where part of the image is assumed to be homogeneous and can be well represented by a constant magnitude. We propose a novel reconstruction algorithm that incorporates this prior knowledge by iteratively enforcing discreteness through Bayesian segmentation regularization. Results on simulated MR images of breast implants and MR angiography images evidence the benefits of the partial discreteness prior when compared to state-of-the-art reconstruction methods.