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Abstract #4448

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

Vinicius P. Campos1,2, Marcelo A.C. Vieira1, and Alessandro Foi3
1Department of Electrical and Computer Engineering, São Carlos School of Engineering, University of São Paulo, São Carlos, Brazil, 2Department of Neurobiology, University of Pittsburgh, Pittsburgh, PA, United States, 3Faculty of Information Technology and Communication Sciences, Tampere University, Tampere, Finland

Synopsis

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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Keywords