Regularized Estimation of Magnitude and Phase of Multi-Coil $B_1$ Field Via Bloch–Siegert $B_1$  Mapping and Coil Combination Optimizations
Parallel excitation requires fast and accurate B1 map estimation. Bloch-Siegert (BS) B1 mapping is very fast and accurate over a large dynamic range. When applied to multi-coil systems, however, this phase-based method may produce low signal-to-noise ratio estimates in low magnitude regions due to localized excitation patterns of parallel excitation systems. Also, the imaging time increases with the number of coils. In this work, we first propose to modify the standard BS B1 mapping sequence so that it avoids the scans required by previous B1 phase estimation methods. A regularized method is then proposed to jointly estimate the magnitude and phase of multi-coil B1 maps from BS B1 mapping data, improving estimation quality by using the prior knowledge of the smoothness of B1 magnitude and phase. Lastly, we use Cramer-Rao lower bound analysis to optimize the coil combinations, to improve the quality of the raw data for B1 estimation. The proposed methods are demonstrated by simulations and phantom experiments.