The present invention relates to an apparatus for multi material decomposition of an object. It is described to provide (310) at least one image of an object. The at least one image is derived from at least one spectral X-ray image of the object, and the at least one image comprises a Photoelectric total attenuation coefficient image and a Compton scattering total attenuation coefficient image. A plurality of Photoelectric attenuation coefficients are provided (320) for a plurality of materials, each Photoelectric attenuation coefficient being associated with a corresponding material. A plurality of Compton scattering attenuation coefficients are provided (330) for the plurality of materials, each Compton scattering attenuation coefficient being associated with a corresponding material. A total volume constraint is set (340) at an image location in the at least one image as a function of the sum of individual volumes of the plurality of materials at the image location. Volume fractions of the plurality of materials are determined (350) at the image location according to an overall function comprising: a Photoelectric total attenuation coefficient at the image location taken from the Photoelectric total attenuation coefficient image; a Compton scattering total attenuation coefficient at the image location taken from the Compton scattering total attenuation coefficient image; the plurality of Photoelectric attenuation coefficients for the plurality of materials; the plurality of Compton scattering attenuation coefficients for the plurality of materials; and the total volume constraint. Data representative of the volume fractions of the plurality of materials is output (360).