Background Removal

Considering the fact that MR scanners typically generate normally distributed white noise [12], the best threshold for separating background noise is determined with the technique of Brummer et al. [7]. In reconstructed MR data, background noise has a Rayleigh distribution [17] given by

where f is the intensity and a is the standard deviation of the white noise. This distribution is observed in the lower intensities of the uncorrected histogram of MR volumes as illustrated in Fig. 3. A bimodal distribution g(f) is obtained if the best fit Rayleigh curve, r (f), is subtracted from the volume histogram, h(f):

We can obtain a minimum error threshold, r, by minimizing an error term er given by

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