Unbiased noise estimation and denoising in parallel magnetic resonance imaging

In magnetic resonance (MR) clinical practice, noise estimation is usually performed on Rayleigh-distributed background (no signal area) of magnitude images. Although noise variance in quadrature MR images is considered spatially independent, parallel MRI (pMRI) techniques as SENSE or GRAPPA generate spatially varying noise (SVN) distribution. In this scenario noise estimation from background may produce biased results. To address these limitations we introduce a novel noise estimation scheme based on local statistics. Our method turns out to be more accurate than the other pMRI noise estimation schemes previously described in the literature. Denoising performances, measured by visual inspection and peak signal-to-noise ratio (PSNR), of Non-Local Means denoising filters (NLM) are considerably improved using SVN-NLM in case of inhomogeneous noise. Furthermore, SVN-NLM behaves as well as standard NLM when homogeneous noise was added, thus proving to be a robust and powerful denoising algorithm for arbitrary MRI datasets.