Bayesian $k$ -Space–Time Reconstruction of MR Spectroscopic Imaging for Enhanced Resolution

A k -space-time Bayesian statistical reconstruction method (K-Bayes) is proposed for the reconstruction of metabolite images of the brain from proton (¹ H) magnetic resonance (MR) spectroscopic imaging (MRSI) data. K-Bayes performs full spectral fitting of the data while incorporating structural (anatomical) spatial information through the prior distribution. K-Bayes provides increased spatial resolution over conventional discrete Fourier transform (DFT) based methods by incorporating structural information from higher resolution coregistered and segmented structural MR images. The structural information is incorporated via a Markov random field (MRF) model that allows for differential levels of expected smoothness in metabolite levels within homogeneous tissue regions and across tissue boundaries. By further combining the structural prior model with a k -space-time MRSI signal and noise model (for a specific set of metabolites and based on knowledge from prior spectral simulations of metabolite signals), the impact of artifacts generated by low-resolution sampling is also reduced. The posterior-mode estimates are used to define the metabolite map reconstructions, obtained via a generalized expectation-maximization algorithm. K-Bayes was tested using simulated and real MRSI datasets consisting of sets of k-space-time-series (the recorded free induction decays). The results demonstrated that K-Bayes provided qualitative and quantitative improvement over DFT methods.