Accelerated parallel magnetic resonance imaging reconstruction using joint estimation with a sparse signal model

Accelerating magnetic resonance imaging (MRI) by reducing the number of acquired k-space scan lines benefits conventional MRI significantly by decreasing the time subjects remain in the magnet. In this paper, we formulate a novel method for Joint estimation from Undersampled LinEs in Parallel MRI (JULEP) that simultaneously calibrates the GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) reconstruction kernel and reconstructs the full multi-channel k-space. We employ a joint sparsity signal model for the channel images in conjunction with observation models for both the acquired data and GRAPPA reconstructed k-space. We demonstrate using real MRI data that JULEP outperforms conventional GRAPPA reconstruction at high levels of undersampling, increasing the peak-signal-to-noise ratio by up to 10 dB.