Solving for non-ideal conditions in two-dimensional Fourier transform magnetic resonance imaging using a generalised inverse transform

Magnetic resonance imaging uses real and complex forms of the Fourier transform and to a lesser degree the Radon transform and their appropriate inverses. Under ideal conditions, these solutions are fast and optimal in the sense of signal-to-noise ratio (S/N). In practice, though, the phase of the signal may not be ideal so that the effective forward transform is no longer a Fourier transform. Using the inverse Fourier transform would then …