Ultrafast 3D Bloch–Siegert B [Formula: see text] ‐mapping using variational modeling

PURPOSE: Highly accelerated B [Formula: see text] ‐mapping based on the Bloch–Siegert shift to allow 3D acquisitions even within a brief period of a single breath‐hold. THEORY AND METHODS: The B [Formula: see text] dependent Bloch–Siegert phase shift is measured within a highly subsampled 3D‐volume and reconstructed using a two‐step variational approach, exploiting the different spatial distribution of morphology and B [Formula: see text] ‐field. By appropriate variable substitution the basic non‐convex optimization problem is transformed in a sequential solution of two convex optimization problems with a total generalized variation (TGV) regularization for the morphology part and a smoothness constraint for the B [Formula: see text] ‐field. The method is evaluated on 3D in vivo data with retro‐ and prospective subsampling. The reconstructed B [Formula: see text] ‐maps are compared to a zero‐padded low resolution reconstruction and a fully sampled reference. RESULTS: The reconstructed B [Formula: see text] ‐field maps are in high accordance to the reference for all measurements with a mean error below 1% and a maximum of about 4% for acceleration factors up to 100. The minimal error for different sampling patterns was achieved by sampling a dense region in k‐space center with acquisition times of around 10–12 s for 3D‐acquistions. CONCLUSIONS: The proposed variational approach enables highly accelerated 3D acquisitions of Bloch–Siegert data and thus full liver coverage in a single breath hold.