Analytic quantification of bias and variance of coil sensitivity profile estimators for improved image reconstruction in MRI

Magnetic resonance (MR) imaging provides a unique in-vivo capability of visualizing tissue in the human brain non-invasively, which has tremendously improved patient care over the past decades. However, there are still prominent artifacts, such as intensity inhomogeneities due to the use of an array of receiving coils (RC) to measure the MR signal or noise amplification due to accelerated imaging strategies. It is critical to mitigate these artifacts for both visual inspection and quantitative analysis. The cornerstone to address this issue pertains to the knowledge of coil sensitivity profiles (CSP) of the RCs, which describe how the measured complex signal decays with the distance to the RC. Existing methods for CSP estimation share a number of limitations: (i) they primarily focus on CSP magnitude, while it is known that the solution to the MR image reconstruction problem involves complex CSPs and (ii) they only provide point estimates of the CSPs, which makes the task of optimizing the parameters and acquisition protocol for their estimation difficult. In this paper, we propose a novel statistical framework for estimating complex-valued CSPs. We define a CSP estimator that uses spatial smoothing and additional body coil data for phase normalization. The main contribution is to provide detailed information on the statistical distribution of the CSP estimator, which yields automatic determination of the optimal degree of smoothing for ensuring minimal bias and provides guidelines to the optimal acquisition strategy.