Image reconstruction from multiple sensors using stein´s principle. Application to parallel MRI

We are interested in image reconstruction when data provided by several sensors are corrupted with a linear operator and an additive white Gaussian noise. This problem is addressed by invoking Stein´s Unbiased Risk Estimate (SURE) techniques. The key advantage of SURE methods is that they do not require prior knowledge about the statistics of the unknown image, while yielding an expression of the Mean Square Error (MSE) only depending on the statistics of the observed data. Hence, they avoid the difficult problem of hyperparameter estimation related to some prior distribution, which traditionally needs to be addressed in variational or Bayesian approaches. Consequently, a SURE approach can be applied by directly parameterizing a wavelet-based estimator and finding the optimal parameters that minimize the MSE estimate in reconstruction problems. Simulations carried out on parallel Magnetic Resonance Imaging (pMRI) images show the improved performance of our method with respect to classical alternatives.