1. A method for reconstructing image component densities of an object, said method comprising: acquiring multi-spectral x-ray tomographic data; performing a material decomposition of the multi-spectral x-ray tomographic data to generate a plurality of material decomposed sinograms; and reconstructing a plurality of material component density images by iteratively optimizing a single functional that includes a joint likelihood term of at least two of the material decomposed sinograms given a material component density reconstruction, wherein the joint likelihood term includes correlation information between the material decomposed sinograms.