Improved detectability in low signal-to-noise ratio magnetic resonance images by means of a phase-corrected real reconstruction

We show that for magnetic resonance (MR) images with signal-to-noise ratio (SNR) < 2 it is advantageous to use a phase-corrected real reconstruction, rather than the more usual magnitude reconstruction. We discuss the results of the phase correction algorithm used to experimentally verify the result. We supplement the existing the literature by presenting closed form expressions (in an MR context) for the probability distribution and first moments of the signal resulting from a magnitude reconstruction.