Some noise properties of 2DFT MR images from asymmetrically sampled data

This report describes noise statistics in 2DFT MR images, expanding the earlier work of Henkelman and others to include variably asymmetric sampling and conjugate synthesis reconstruction. The effects of low-order polynomial and Fourier phase correction used with conjugate synthesis are also explicitly considered. This analysis shows that complex images obtained by conjugate synthesis have an elliptical noise distribution, with the smaller axis corresponding to the imaginary image channel. Derivations and simulations predict a ratio of mean to standard deviation in the background of magnitude images varying from the known value of square root of pi/(4 - pi) (approximately 1.91) for full symmetry to square root of 2/(pi - 2) (approximately 1.32) at fully asymmetric or half-echo sampling; these predictions are validated over a range of asymmetry by experimental measurements. These results are important for predicting and interpreting image noise when using asymmetric sampling.