Within computed tomography (CT), increased image quality comes at the expense of amplified radiation exposure to patients. To reduce radiation exposure, techniques have emerged which use iterative methods to reconstruct images from limited-angle or sparse-view CT data. Superiorization is a recently proposed framework which “superiorizes” an existing reconstruction algorithm with respect to some secondary objective function. As a result, superiorization can reduce artifacts in the reconstructed image caused by sparse-view and/or limited-angle data. Within certain constraints, the superiorization method guarantees a reconstruction which fits the data equally well as the original reconstruction. More importantly, superiorization is expected to produce an image with higher quality. Existing research within superiorization has been confined to reconstructing images given data generated from monoenergetic X-ray beams. Despite the promise of this existing research, polyenergetic X-ray beams are common in clinical settings and existing methods need to be extended to handle polyenergetic data. To this end, our research goal was to extend the superiorization method to reconstruct images from polyenergetic data, using total variation (TV) and anistropic total variation (ATV) as the secondary objectives to be superiorized. In addition to successfully reconstructing images from polyenergetic data, we also demonstrate our method is capable of reconstructing images with “missing” data which is a result of sparse-view and limited-angle scans. This research further extends the potential of utilizing iterative methods in CT and thus reducing radiation exposure to patients.