Water-fat separation for fast spin echo imaging in an inhomogeneous field with progressive encoding

nnnnnnnA method to separate two chemically-shifted components of water (w) and fat (f) signals by: (i) estimating the field inhomogeneity β through a treatment of the residuals of the Moore-Penrose solution of the following equations: cos(αβ)*w+cos [α(1+β)]*f=real (I) and sin(αβ)*w+sin [α(1+β)]*f=imaginary (I), and (ii) using the estimated β to determine the resulting solution for w and f from the original input signals I.