An apparatus and method are described using a forward model to correct pulse pileup in spectrally resolved X-ray projection data from photon-counting detectors (PCDs). To calibrate the forward model, which represents each order of pileup using a respective pileup response matrix (PRM), an optimization search determines the elements of the PRMs that optimize an objective function measuring agreement between the spectra of recorded counts affected by pulse pileup and the estimated counts generated using forward model of pulse pileup. The spectrum of the recorded counts in the projection data is corrected using the calibrated forward model, by determining an argument value that optimizes the objective function, the argument being either a corrected X-ray spectrum or the projection lengths of a material decomposition. Images for material components of the material decomposition are then reconstructed using the corrected projection data.