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Is Perfect Filtering Enough Leading to Perfect Phase Correction for dMRI data?

Being complex-valued and low in signal-to-noise ratios, magnitude-based diffusion MRI is confounded by the noise-floor that falsely elevates signal magnitude and incurs bias to the commonly used diffusion indices, such as fractional anisotropy (FA). To avoid noise-floor, most existing phase correction methods explore improving filters to estimate the noise-free background phase. In this work, after diving into the phase correction procedures, we argue that even a perfect filter is insufficient for phase correction because the correction procedures are incapable of distinguishing sign-symbols of noise, resulting in artifacts (\textit{i.e.}, arbitrary signal loss). With this insight, we generalize the definition of noise-floor to a complex polar coordinate system and propose a calibration procedure that could conveniently distinguish noise sign symbols. The calibration procedure is conceptually simple and easy to implement without relying on any external technique while keeping distinctly effective.

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