On the noise in "augmented T1-weighted steady state magnetic resonance imaging"

Recently, Ye and colleagues proposed a method for "augmented T1-weighted imaging " (aT(1)W). The key operation is a complex division of gradient-echo (GRE) images obtained with different flip angles. Ye and colleagues provide an equation for the standard deviation of the obtained aT(1)W signal. Here, we show that this equation leads to wrong values of the standard deviation of such an aT(1)W signal. This is demonstrated by Monte Carlo simulations. The derivation of the equation provided by Ye and colleagues is shown to be erroneous. The error consists of a wrong handling of random variables and their standard deviations and of the wrong assumption of correlated noise in independently acquired GRE images. Instead, the probability distribution obtained with the aT(1)W-method should have been carefully analyzed, perhaps on the basis of previous literature on ratio distributions and their normal approximations.