A blind deconvolution approach for pseudo CT prediction from MR image pairs

Predicting a CT image or a map of the linear attenuation coefficients from the information provided by magnetic resonance imaging (MRI) is a challenging task. This problem is of significant importance for combined positron emission tomography (PET)/MRI scanners, as quantitative PET image reconstruction requires an attenuation map. In PET/CT this attenuation map is derived from the CT scan or from a rotating source, however, current PET/MR systems can not directly measure attenuation images - and indeed it is desirable to save the patient from the additional radiation exposure. Recent approaches tackle this problem by using MR sequences with ultra-short echo times (UTE). At the price of lower effective image resolution, the UTE image yields signal from bone and therefore provides valuable information for calculating the attenuation map. We propose a novel approach to this problem based on nonnegative blind deconvolution and present the first method that explicitly models the image degradation of the UTE image. Incorporating prior knowledge such as smoothness and a novel orthogonality constraint alleviates the deconvolution process. Due to its probabilistic formulation our approach allows hyperparameter estimation and is therefore parameter-free.