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

PurposeRegularizing parallel magnetic resonance imaging (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 that minimizes the multichannel 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. TheoryWe derive a weighted MSE criterion appropriate for data-preserving regularized parallel imaging reconstruction and the corresponding weighted Stein's unbiased risk estimate. We describe a Monte Carlo approximation of the weighted Stein's unbiased risk estimate that uses two evaluations of the reconstruction method per candidate parameter value. MethodsWe reconstruct images using the denoising sparse images from GRAPPA using the nullspace method (DESIGN) and L-1 iterative self-consistent parallel imaging (L-1-SPIRiT). We validate Monte Carlo Stein's unbiased risk estimate 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. ResultsOur method selects nearly MSE-optimal regularization parameters for both DESIGN and L-1-SPIRiT over a range of noise levels and undersampling factors. ConclusionThe proposed method automatically provides nearly MSE-optimal choices of regularization parameters for data-preserving nonlinear parallel MRI reconstruction methods. Magn Reson Med 71:1760-1770, 2014. (c) 2013 Wiley Periodicals, Inc.