Alias subtraction more efficient than conventional zero-padding in the Fourier-based calculation of the susceptibility induced perturbation of the magnetic field in MR.

Forward calculation of the susceptibility induced field shift by Fourier-based procedures requires spatial zero-padding to prevent aliasing artifacts (periodic wrap-around). Padding with a factor of two gives accurate results, however, halves the maximal attainable resolution, and slows down the calculation, which may hamper the feasibility of real-time calculations. Herein is proposed to first perform the calculation at the original resolution--allowing aliasing-and to remove aliasing with an additional convolution in a lower resolution, to alleviate these restrictions regarding memory size and calculation speed, a procedure we termed "virtual" zero-padding. Virtual zero-padding was numerically and experimentally tested and validated with conventional zero-padding and the analytical solution (in the case of spheres) on several phantoms. A demonstration of the increased efficiency is given by implementing virtual zero-padding in a dynamic calculation procedure. The improved efficiency is expected to be relevant regarding the ongoing increase in spatial and temporal resolution in ultra-high-field MRI. Procedures are presented for circular convolution using the discrete Green's function and k-space filtering using the continuous Green's function.