Noise estimation and removal in MR imaging: The variance-stabilization approach

We develop optimal forward and inverse variance-stabilizing trans formations for the Rice distribution, in order to approach the problem of magnetic resonance (MR) image filtering by means of standard denoising algorithms designed for homoskedastic observations. Further, we present a stable and fast iterative procedure for robustly estimating the noise level from a single Rician-distributed image. At each iteration, the procedure exploits variance stabilization composed with a homoskedastic variance-estimation algorithm. Theoretical and experimental study demonstrates the success of our approach to Rician noise estimation and removal through variance stabilization. In particular, we show that the performance of current state-of-the-art algorithms specifically designed for Rician distributed data can be matched by combining conventional algorithms designed for additive white Gaussian noise with optimal variance-stabilizing transformations.