Rician bias correction

MRI magnitude images are contaminated with Rician noise that introduces a Rician bias in the estimated parameters if not accounted for. The Rician bias is inversely proportional to the signal to noise ratio (SNR), that is, the lower the SNR the higher the bias and vice versa, see ACID paper for more details (ACID-Toolbox paper (preprint)). The ACID toolbox offers two approaches for Rician bias correction that must not be used together:

1. Rician bias correction module:

The implemented “Rician bias correction” module works with the M2 approach that operates directly on the acquired dMRI data and corrects them by calculating the second moment of the non-central chi distribution to estimate the true voxel intensity.

The inputs are the following:

• Input images: the acquired dMRI data

• Noise estimate: an estimate of the noise in the acquired dMRI data

• RBC correction types:

  • “RBC Koay Ades-Aron”: Corrects all voxel independent of the SNR.
  • “RBC Koay”: Corrects only voxels with SNRs between 1.913 and 10.

• Effective number of channels: the effective number of channels that depends on the MRI sequence (e.g., for a parallel imaging with a PAT= 2 it is 2)

2. Rician bias in the NLLS DKI / axisymmetric DKI:

The implemented Rician bias correction in the NLLS DKI and axisymmetric DKI fits is based on the first moment of the non-central chi distribution and refines the signal model prediction during fitting. The inputs are the following:

• Noise estimate: an estimate of the noise in the acquired dMRI data

• Effective number of channels: the effective number of channels that depends on the MRI sequence (e.g., for a parallel imaging with a PAT= 2 it is 2)

• Noise map: a noise map that contains a noise estimate for every image voxel