Optimized linear combinations of channels for complex multiple-coil B1 field estimation with Bloch-Siegert B1 mapping in MRI

Bloch-Siegert B1 mapping for multiple-channel parallel excitation systems usually produces noisy estimates in low intensity regions. Methods that use linear combinations of multiple coils have been proposed to mitigate this problem. However, little work has been done to optimize these coil combinations to improve the signal-to-noise ratio of B1 mapping in a robust way. In this paper, we propose a Cramer-Rao Lower Bound analysis based method to optimize the coil combination matrix by minimizing the variance of B1 map estimation for the previously proposed Bloch-Siegert B1 mapping method. We illustrate how optimizing the coil combinations yields improved B1 estimates in a simulation of brain imaging with a 3T MRI scan.