Bias correction for non-stationary noise filtering in MRI

The aggregation of non-stationary distributed magnetic resonance imaging (MRI) samples results in a systematic bias that should be corrected prior to any further numerical processing, such as quantitative analysis. In this paper, we analytically derive two formulas to compensate the bias from aggregated non-stationary non-central chi (nc-χ) distributed random variables. As a proof-of-concept, we reformulate the unbiased non-local means (UNLM) filtering scheme to handle non-stationary nc-χ and particularly non-stationary Rician distributed MR data. The proposals are validated over synthetic and real parallel accelerated MR reconstructions leading to a considerable reduction of inherent bias component over the state-of-the-art UNLM approach.