Monte Carlo SURE-Based Parameter Selection for Parallel Magnetic Resonance Imaging Reconstruction

Purpose: Regularizing parallel MRI reconstruction significantly improves image quality but requires tuning parameter selection. We propose a Monte Carlo method for automatic parameter selection based on Stein’s unbiased risk estimate (SURE) that minimizes the multi-channel k-space mean squared error (MSE). We automatically tune parameters for image reconstruction methods that preserve the undersampled acquired data, which cannot be accomplished using existing techniques. Theory: We derive a weighted MSE criterion appropriate for data-preserving regularized parallel imaging reconstruction and the corresponding weighted SURE. We describe a Monte Carlo approximation of the weighted SURE that uses two evaluations of the reconstruction method per candidate parameter value. Methods: We reconstruct images using the sparsity-promoting methods DESIGN and L1-SPIRiT. We validate Monte Carlo SURE against the weighted MSE. We select the regularization parameter using these methods for various noise levels and undersampling factors and compare the results to those using MSE-optimal parameters. Results: Our method selects nearly MSE-optimal regularization parameters for both DESIGN and L1SPIRiT over a range of noise levels and undersampling factors. Conclusion: The proposed method automatically provides nearly MSE-optimal choices of regularization parameters for data-preserving nonlinear parallel MRI reconstruction methods.