A penalized likelihood approach to magnetic resonance image reconstruction

Currently, images acquired via magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI) technology are reconstructed using the discrete inverse Fourier transform. While computationally convenient, this approach is not able to filter out noise. This is a serious limitation because the amount of noise in MRI and fMRI can be substantial. In this paper, we propose an alternative approach to reconstruction, based on penalized likelihood methodology. In particular, we focus on non-linear shrinkage estimators and show that this approach achieves a great reduction in integrated mean squared error (IMSE) of the estimated image with respect to the currently used estimator. This approach is extremely fast and easy to implement computationally. In addition, it can be combined with various alternative approaches to MR image reconstruction and can be easily adapted to other, non-MRI contexts, in which the observed data and the quantities of interest are related via a linear transform.