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. 1995 Dec;34(6):910-4.
doi: 10.1002/mrm.1910340618.

The Rician distribution of noisy MRI data

H Gudbjartsson  1 , S Patz
Affiliations

The Rician distribution of noisy MRI data

H Gudbjartsson et al. Magn Reson Med. 1995 Dec.

Erratum in

  • Magn Reson Med 1996 Aug;36(2):332

Abstract

The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution. Low signal intensities (SNR < 2) are therefore biased due to the noise. It is shown how the underlying noise can be estimated from the images and a simple correction scheme is provided to reduce the bias. The noise characteristics in phase images are also studied and shown to be very different from those of the magnitude images. Common to both,however, is that the noise distributions are nearly Gaussian for SNR larger than two.

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Figures

FIG. 1
FIG. 1
The Rician distribution of M for several signal to noise ratios, A/σ, and the corresponding means.
FIG. 2
FIG. 2
The distribution of the phase noise for several signal to noise ratios, A/σ. The Gaussian approximation is shown with a dotted line for A/σ = 3.
FIG. 3
FIG. 3
The distribution of the corrected pixel intensity, Ã (bold), compared with the Rician distribution of M for several signal to noise ratios. The mean of the corrected distribution, A, is shown with a vertical line.
FIG. 4
FIG. 4
The distribution of the corrected pixel power (7), Ã2 (bold), compared with the distribution of the measured power, M2, for several signal to noise ratios. The mean of the corrected distribution, A∼2¯ = A2, is shown with a vertical line.
FIG. 5
FIG. 5
Histogram of the pixel intensity from a region with N = 5000 pixels. The solid line is the corresponding Rayleigh distribution, estimated from the mean of the histogram.
FIG. 6
FIG. 6
The normalized autocorrelation function of the image noise shows some extra correlation due to the Fermi lowpass filtering of the data. Otherwise the agreement with Eq. [14] is good.
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References

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