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A novel quasi-linearization method was developed for CT image reconstruction in scanners with a multi-energy detector system. The non-linear equation relating material attenuation coefficients to measured data was reduced to a system of linear equations by means of piece-wise constant approximation of attenuation functions. A material decomposition algorithm was proposed to obtain a physically meaningful solution of this system for the case of N = 2 (dual-energy CT scanners). Image reconstruction methods (the new one and the classical filtered backprojection with beam-hardening correction) were implemented to measured CT data. The new method consistently provides more accurate density results in image reconstruction for the objects containing materials with significantly different attenuation coefficients.