Knowledge of X-ray spectrum is essential in many applications of X-ray computed tomography (CT)

such as spectral CT imaging

beam hardening correction

quantitative analysis of CT images

etc. But the spectrum of an X-ray source is hard to measure with X-ray spectrometer directly due to strong X-ray flux emitted. Other kind of attractive methods are indirect

which estimate the x-ray spectrum from a set of projection data of phantoms with different thicknesses. In indirect methods

the spectrum estimation problem is boiled down to a set of ill conditioned linear equations. To acquire accurate spectrum

a large number of measurements are required

which needs heavy workload. To overcome the abovementioned obstacle

we propose a novel X-ray spectrum estimation method that first fits the polychromatic projection curve with quadratic rational fraction

and then estimate the X-ray spectrum from the sampling points of the fitted curve. As a quadratic rational fraction includes only three parameters

only a few measurements are needed to get an accurate fitting. Numerical experiments show that the accuracy of the X-ray spectrum estimated through the proposed method with three measurements is commensurate to that estimated with tradition method from over a dozen of measurements. Therefore

the proposed method lessens the workloads effectively.