Vectorial non-local total variation regularization for calibration-free parallel MRI reconstruction

In this work we present a calibration-free parallel magnetic resonance imaging (pMRI) reconstruction approach by exploiting the fact that image structures typically tend to repeat themselves in several locations in the image domain. We use this prior information along with the correlation that exists among the different MR images, which are acquired from multiple receiver coils, to improve reconstructions from under-sampled data with arbitrary k-space trajectories. To accomplish this, we follow a variational approach and cast the pMRI reconstruction problem as the minimization of an energy functional that involves a vectorial non-local total variation (NLTV) regularizer. Further, to solve the posed optimization problem we propose an iterative algorithm which is based on a variable splitting strategy. To assess the reconstruction quality of the proposed method, we provide comparisons with alternative techniques and show that our results can be very competitive.