A method of decomposition of projection data is provided, wherein such projection data includes input projection data acquired using at least two x-ray spectra for a scanned object, including low energy projection data (P.sub.L) and high energy projection data (P.sub.H); the method comprises solving the projections P.sub.L and P.sub.H to determine a photoelectric line integral (A.sub.p) component of attenuation and a Compton line integral (A.sub.c) component of attenuation of the scanned object using a multi-step fitting procedure and constructing a Compton image I.sub.c and a photoelectric image I.sub.p from the Compton line integral and photoelectric line integral.