Parallel MR image reconstruction by adaptively weighted H∞ optimization

H_∞ optimal reconstruction [1] is a new method we recently proposed to overcome the difficulties in SENSE reconstruction of parallel MRI when the coil sensitivity map is uncertain and ill-conditioned. However, the weighting selection in this method is ad hoc and may involve tedious trial and error. To overcome this problem, this paper proposes a novel adaptively weighted H_∞ optimal reconstruction method for image reconstruction of parallel MRI. The novelty is two folds. First, the weighting factor ?? is considered as a unique adaptive value for each individual pixel instead of a global value. Second, the selection of ?? is based on an optimization instead of trial and error experiments. The proposed method enhances the performance of the H_∞ optimal reconstruction by adaptive weighting and automates the weighting selection by minimizing generalized cross validation (GCV) function.