SURE-based automatic parameter selection for ESPIRiT calibration

ESPIRiT is a parallel imaging method that estimates coil sensitivity maps from the auto-calibration region (ACS). This requires choosing several parameters for the optimal map estimation. While fairly robust to these parameter choices, occasionally, poor selection can result in reduced performance. The purpose of this work is to automatically select parameters in ESPIRiT for more robust and consistent performance across a variety of exams.

By viewing ESPIRiT as a denoiser, Stein's unbiased risk estimate (SURE) is leveraged to automatically optimize parameter selection in a data-driven manner. The optimum parameters corresponding to the minimum true squared error, minimum SURE as derived from densely sampled, high-resolution, and non-accelerated data and minimum SURE as derived from ACS are compared using simulation experiments. To avoid optimizing the rank of ESPIRiT's auto-calibrating matrix (one of the parameters), a heuristic derived from SURE-based singular value thresholding is also proposed.

Simulations show SURE derived from the densely sampled, high-resolution, and non-accelerated data to be an accurate estimator of the true mean squared error, enabling automatic parameter selection. The parameters that minimize SURE as derived from ACS correspond well to the optimal parameters. The soft-threshold heuristic improves computational efficiency while providing similar results to an exhaustive search. In-vivo experiments verify the reliability of this method.

Using SURE to determine ESPIRiT parameters allows for automatic parameter selections. In-vivo results are consistent with simulation and theoretical results.