Evaluation of Primal-Dual Splitting Algorithm for MRI Reconstruction Using Spatio-Temporal Structure Tensor and L1-2 Norm

Abstract

Magnetic resonance imaging (MRI) is an essential medical imaging technique which is widely used for medical research and diagnosis. Dynamic MRI provides the observed object visualization through time and results in a spatiotemporal signal. The image sequences often contain redundant information in both spatial and temporal domains. To utilize this characteristic, we propose a spatio-temporal reconstruction approach based on compressive sensing theory. We apply spatio-temporal structure tensor using nuclear norm, in addition to the wavelet sparsity regularization. The spatio-temporal structure tensor is a matrix that consists of gradient components of the MRI data w.r.t the spatial and temporal domains. For the wavelet sparsity, we use L1 – L2 instead of L1 norm. We propose the algorithm using primaldual splitting (PDS) approach to solve the convex optimization problem. In the experiment, we investigate the potential benefit of adding the two regularizations to the compressive sensing problem. The algorithm is compared with PDSbased algorithm using conventional regularizations, i.e., wavelet sparsity and total variation. Our proposed algorithm performs superior results in terms of reconstruction accuracy and visual quality.