A method of generating a susceptibility map of an object utilizes a regularizing inverse function, oversampling k-space, removing external phase noise and rapid phase change effects, accounting for the known geometry of the object, and using modified SWI phase data to generate reasonable susceptibility maps and digital images therefrom, such as SWI images. The inventors refers to the inventive methods set forth herein as Susceptibility Weighted Imaging and Mapping (SWIM).