1. A method for determining a spatial distribution of susceptibility in a subject using a magnetic resonance imaging (MRI) system, wherein the method includes steps comprising: a) directing the MRI system to acquire imaging data from an imaging volume within a subject, wherein the imaging volume is subject to both background fields (B B ) originating outside the imaging volume and local fields (B L ) originating from tissue within the imaging volume; b) selecting a size and non-central compute point for an extended Poisson kernel to be applied to the imaging data; c) subtracting from a delta function to control the background fields (B B ) but not the local fields (B L ); and d) producing a susceptibility report attributable to the local fields (B L ).