Least squares reconstruction of non-linear RF phase encoded MR data

The numerical feasibility of reconstructing MRI signals generated by RF coils that produce B1 fields with a non-linearly varying spatial phase is explored.

A global linear spatial phase variation of B1 is difficult to produce from current confined to RF coils. Here we use regularized least squares inversion, in place of the usual Fourier transform, to reconstruct signals generated in B1 fields with non-linear phase variation.

RF encoded signals were simulated for three RF coil configurations: ideal linear, parallel conductors and, circular coil pairs. The simulated signals were reconstructed by Fourier transform and by regularized least squares.

The Fourier reconstruction of simulated RF encoded signals from the parallel conductor coil set showed minor distortions over the reconstruction of signals from the ideal linear coil set but the Fourier reconstruction of signals from the circular coil set produced severe geometric distortion. Least squares inversion in all cases produced reconstruction errors comparable to the Fourier reconstruction of the simulated signal from the ideal linear coil set.

MRI signals encoded in B1 fields with non-linearly varying spatial phase may be accurately reconstructed using regularized least squares thus pointing the way to the use of simple RF coil designs for RF encoded MRI.