Two-stage neural network models for MR image reconstruction from sparsely sampled k-space

A novel approach for magnetic resonance imaging (MRI) reconstruction using a two-stage neural network model, involving regularization techniques, is herein presented. The MRI reconstruction problem is considered when the k-space is sparsely scanned. 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 in such a case is to reduce the measurement time by omitting as many scanning trajectories as possible. The proposed model involves a regularized Kohonen feature map (SOFM) in the first stage which aims at quantizing the input variable space into smaller regions representative of the input space probability distribution and preserving its original topology, while increasing, on the other hand, cluster distances. This is achieved through adapting not only the winning neuron and its neighboring neurons weights but, also, loosing neurons weights during map´s convergence phase. During convergence phase of the map, a group of support vector machines (SVM), associated with its codebook vectors, is simultaneously trained in an online fashion so that each SVM learns to respond when the input data belong to the topological space represented by its corresponding codebook vector. Moreover, these SVMs follow a task specific regularization strategy which aims at incorporating additional information in their training process. It is found that such a model results in an improved image reconstruction performance very favourably compared to the one obtained by the trivial zero-filled k-space approach or traditional more sophisticated interpolation approaches.