Sure-based parameter selection for parallel MRI reconstruction using GRAPPA and sparsity

New methods have been developed for parallel MRI reconstruction combining GRAPPA and sparsity. One impediment to the practical application of such methods is selecting a regularization parameter that acceptably balances the contributions of GRAPPA and sparsity. We propose a broadly applicable Monte-Carlo-based approximation to Stein's unbiased risk estimate (SURE) for a suitable weighted mean-squared error (WMSE) metric. Applying this approximation to predict the WMSE-optimal tuning parameter for sparsity-based reconstruction, we are able to tune our parameter to achieve nearly MSE-optimal performance. In our simulations, we vary the noise level in the simulated data and use our Monte-Carlo method to tune the reconstruction to the noise level automatically.