Novel CdTe photon counting x-ray detectors (PCXDs) have been developed for very high count rates [1-4] suitable for x-ray micro computed tomography (μCT) scanners. It counts photons within each of J energy bins. In this study, we investigate use of the data in these energy bins for material decomposition using an image domain approach. In this method, one image is reconstructed from projection data of each energy bin; thus, we have J images from J energy bins that are associated with attenuation coefficients with a narrow energy width. We assume that the spread of energies in each bin is small and thus that the attenuation can be modeled using an effective energy for each bin. This approximation allows us to linearize the problem, thus simplify the inversion procedure. We then fit J attenuation coefficients at each location x by the energy-attenuation function  and obtain either (1) photoelectric and Compton scattering components or (2) 2 or 3 basis-material components. We used computer simulations to evaluate this approach generating projection data with three types of acquisition schemes: (A) five monochromatic energies; (B) five energy bins with PCXD and an 80 kVp polychromatic x-ray spectrum; and (C) two kVp with an intensity integrating detector. Total attenuation coefficients of reconstructed images and calculated effective atomic numbers were compared with data published by National Institute of Standards and Technology (NIST). We developed a new materially defined "SmileyZ" phantom to evaluate the accuracy of the material decomposition methods. Preliminary results showed that material based 3-basis functions (bone, water and iodine) with PCXD with 5 energy bins was the most promising approach for material decomposition.