Variance stabilization of noncentral-chi data: Application to noise estimation in MRI

A variance-stabilizing transformation (VST) specifically designed for noncentral-chi (nc-x) data is presented. The VST is derived to generate Gaussian-like distributed variates from nc-x data. Two methods are proposed: (1) an analytic asymptotic model for high SNR; and (2) a robust numerical model to improve the performance for low SNR. As an application and proof of concept, the VST is used for the estimation of non-stationary noise fields in multiple coil MRI acquisitions. It is validated over accelerated data reconstructed using GRAPPA. The method is compared to the main state-of-the-art methods. Numerical results confirm the robustness of the method and its better performance for the whole range of SNRs.