X-ray spectra estimated from the numerical phantom at different numbers of primary photon events. (a, c, e) use direct matrix inversion to obtain the material images for the spectrum estimation, whereas (b, d, f) use a noise-reduced dual-energy material decomposition method (i.e., iterative image-domain method) for the spectrum estimation. The numbers of the primary photon events used in the numerical simulations of the low-energy CT scans for (a, b), (c, d), and (e, f) are , , and , respectively. For each of the dual-energy CT scans, the numbers of the photon events of the high-energy CT scans are half of the respective low-energy CT scans.