Improved Bayesian MRI reconstruction involving neural priors based on a regularization approach

The goal of this paper is to present the development of a new reconstruction methodology for restoring magnetic resonance images (MRI) from reduced scans in k-space. The proposed approach considers the combined use of regularized neural network models and Bayesian restoration, in the problem of MRI image extraction from sparsely sampled k-space, following several different sampling schemes, including spiral and radial. Effective solutions to this problem are indispensable especially when dealing with MRI of dynamic phenomena since then, rapid sampling in k-space is required. The goal is such a case is to make measurement time smaller by reducing scanning trajectories as much as possible. In this way, however, underdetermined equations are introduced and poor image reconstruction follows. It is suggested here that significant improvements could be achieved concerning quality of the extracted image, by judiciously applying regularization based neural networks and Bayesian estimation methods to the k-space data. More specifically, it is demonstrated that regularization based neural network techniques could construct efficient priors and introduce them in the procedure of Bayesian reconstruction. These regularized ANN priors are independent of specific image properties and probability distributions. They are based on training supervised multilayer perceptron (MLP) regularized neural filters to estimate the missing samples of complex k-space and thus, to improve k-space information capacity. Such a neural filter based prior is integrated to the maximum likelihood procedure involved in the Bayesian reconstruction. It is found that the proposed methodology leads to enhanced image extraction results favorably compared to the ones obtained by the traditional Bayesian MRI reconstruction approach as well as by the pure MLP based reconstruction approach.