Optimized variance-stabilizing and exact unbiased inverse transforms for the non-central Chi distribution: application in MRI image denoising

Motivation: Noise in magnitude MR images follows a non-central Chi (nc-χ) distribution with non-uniform variance and an intrinsic positive bias. Thus, usual denoising algorithms (for additive Gaussian noise) may perform suboptimally. Goal(s): Elaborate a pair of mathematical transformations that stabilize noise and allow any Gaussian denoiser to be used. Approach: We presented a novel pair of optimized variance-stabilizing (VST) and exact unbiased inverse (EUI) transformations for the nc-χ distribution. Results: The results evidence the applicability of our proposal, in which standard denoising algorithms for additive Gaussian noise, when plugged within the proposed three-step VST framework, matches/outperforms algorithms specifically designed for nc-χ noise. Impact: Magnitude image is the most common data format in MRI clinical settings. Our method allows denoising of magnitude MRI in a way that one can properly use any off-the-shelf Gaussian denoiser without the need to modify its core algorithm.