Self-Calibrating Nonlinear Reconstruction Algorithms for Variable Density Sampling and Parallel Reception MRI

Compressed Sensing has allowed a significant reduction of acquisition times in MRI, especially in the high resolution (e.g., 400 μm) context. However, in this setting CS must be combined with parallel reception as multichannel coil acquisitions maintain high input signal-to-noise ratio (SNR). To get rid of usual parallel imaging limitations (output SNR loss), non-Cartesian trajectories provide a gain in sampling efficiency in the CS context. In this paper, we propose a self-calibrating MRI reconstruction framework that handles variable density sampling. Low resolution sensitivity maps are estimated from the low frequency k-space content using an original and fast method while MR images are reconstructed using a nonlinear iterative algorithm, which promotes sparsity in the wavelet domain. As regards the optimization task, we compare three first-order proximal gradient methods: Forward Backward (FB), Fast Iterative Soft Thresolding Algorithm (FISTA) and Proximal Optimized Gradient Method (POGM) and evaluate their respective convergence speed. Comparison with state-of-the-art (i.e., ℓ
_l
-ESPIRiT) suggests that our self-calibrating POGM-based algorithm outperforms current approaches both in terms of image quality and computing time on several acquired data collected at 7 Tesla and we will focus more specifically on prospective non-Cartesian 8-fold accelerated in vivo Human brain data.