Noise estimation for the velocity in MRI phase-contrast

Abstract

The purpose of this study is to estimate the precision or statistical variability of the velocity measurements computed from MRI phase-contrast. From the analytical probability density function (PDF) of the phase in the signal we obtain the PDF of the velocity by means of an auto-convolution. This PDF allows the estimation of the precision of the velocity, important for the correct interpretation of the many parameters that are based on it. We show that for high Signal-to-Noise Ratio (SNR) voxels, the distribution is well approximated by a Gaussian distribution. On the other hand, this is not true for lower SNR voxels, where the distribution adopts a form in between the Gaussian and the uniform distributions. This was confirmed empirically. Also, knowing the PDF on a coil by coil basis it is possible to combine the data from multiple coils in an optimal way. We showed that the optimal combination reduces the resulting global variability of the velocity, in comparison with the commonly used Weighted Mean or with a SENSE reconstruction with R = 1.