Abstract: A method of phase unwrapping by solving the Poisson equation using a weighted iterative algorithm, for use when separating spectral component with magnetic resonance imaging systems. The solution of the Poisson equation is expedited by using a weighting matrix obtained by calculating the average noise level of an in-phase image and using 3-5 times the noise level as a threshold with only pixel intensity levels above the threshold being set equal to one and the other pixels being set to zero. The pixels on the weight matrix are also set to zero according to the size differences of the phase offset per pixel either in the row or column direction. The solution of the Poisson equation is then uniquely operated on to remove a constant (bias) and to improve the fit.