A method for producing a quantitative susceptibility map using magnetic resonance imaging, the steps of the method comprising: (a) providing to a computer system, magnetic resonance data acquired with an MRI system; (b) generating with the computer system, a field shift map from the magnetic resonance data, the field shift map depicting susceptibility-induced resonance frequency shifts in a volume; (c) generating with the computer system, multiresolution field shift map data by processing the field shift map in order to generate a plurality of field shift maps each with a different spatial resolution associated with a different resolution layer; (d) generating with the computer system for each resolution layer, local field shift map data by dividing the field shift map associated with a given resolution layer into a plurality of local field shift maps, each local field shift map corresponding to a subvolume of the volume; (e) generating with the computer system for each resolution layer, a local susceptibility map for each subvolume by performing a quantitative susceptibility mapping inversion algorithm on each local field shift map associated with a given resolution layer using the computer system; (f) forming with the computer system, multiresolution susceptibility map data by combining the local susceptibility maps for each resolution layer using the computer system in order to generate a plurality of composite susceptibility maps each depicting quantitative values of susceptibility in the volume for each resolution layer; and (g) forming a susceptibility map by combining the plurality of susceptibility maps in the multiresolution susceptibility map data. (a) providing to a computer system, magnetic resonance data acquired with an MRI system; (b) generating with the computer system, a field shift map from the magnetic resonance data, the field shift map depicting susceptibility-induced resonance frequency shifts in a volume; (c) generating with the computer system, multiresolution field shift map data by processing the field shift map in order to generate a plurality of field shift maps each with a different spatial resolution associated with a different resolution layer; (d) generating with the computer system for each resolution layer, local field shift map data by dividing the field shift map associated with a given resolution layer into a plurality of local field shift maps, each local field shift map corresponding to a subvolume of the volume; (e) generating with the computer system for each resolution layer, a local susceptibility map for each subvolume by performing a quantitative susceptibility mapping inversion algorithm on each local field shift map associated with a given resolution layer using the computer system; (f) forming with the computer system, multiresolution susceptibility map data by combining the local susceptibility maps for each resolution layer using the computer system in order to generate a plurality of composite susceptibility maps each depicting quantitative values of susceptibility in the volume for each resolution layer; and (g) forming a susceptibility map by combining the plurality of susceptibility maps in the multiresolution susceptibility map data.