Keywords: Signal Modeling, Data Processing, Denoising, Noise, Variance-stabilizing, VST, exact unbiased inverse, bias, non-central Chi, Rician, BM4D
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.
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