MRI field-shift calculation with virtual Zero-Padding

An efficient implementation of the Fourier-based procedure to calculate the susceptibility-induced field-shift if an object with known susceptibility distribution is placed within a strong homogeneous magnetic field (B0).
The original published procedures (k-space filtering by Salomir in 2003, and circular convolution by Jenkinson in 2004) needed zero-padding to prevent aliasing (circular wrap-around). In this implementation, however, aliasing is removed by estimating this artifact using additional convolutions in a lower resolution.
The methods are very efficient since the aliasing-prevention is decoupled from the convolution of the Region Of Interest. We refer to this procedure as 'virtual Zero-Padding (vZP)'.
Here two calculation functions are presented, one for Circular Convolution (CC), one for k-space filtering (KF).
The article describing the principle of low resolution aliasing subtraction:
Job G. Bouwman, Chris J.G. Bakker. "Alias subtraction more efficient than conventional zero-padding in the Fourier based calculation of the susceptibility induced perturbation of the magnetic field in MR (2012) in "Magnetic Resonance in Medicine" (in press).
Please refer to this article when using this script.

Added a script (FBFC_example.m) for demonstration of the functions FBFC_CC_vZP and FBFC_KF_vZP. This script makes use of the function (FBFC_CC_no_padding.m).