X-ray computed tomography (XCT) is indispensable for mapping the structure of both people and objects, however, it is difficult to get quantitative voxel grey values. One important reason is the interactions of polychromatic x-rays which are ignored by most XCT reconstruction algorithms. A critical component enabling reconstruction algorithms to correctly deal with polychromatic x-rays is the x-ray attenuation model, which describes how the strength of interaction between x-rays and matter varies with energy. Even a relatively straightforward x-ray attenuation model, which for us is the Alvarez-Macovski (AM) model, provides great benefits and brings us closer to quantitative XCT. The AM model can be used as part of a unconventional dual spectrum/dual energy XCT (DECT) scheme. Usually, this requires two scans with different x-ray spectra. We use a recently discovered statistical property of x-rays in commonly used energy integrating detectors to carry out DECT using only a single x-ray spectrum. This is possible because when the detectors are set to record each measurement multiple times and generate both the variance and mean data, the two sets of data contain independent spectral information. We can then use the variance and mean sinograms as the two inputs in an AM model based DECT algorithm and generate artefact free, quantitative XCT tomograms (see Figure 1). Furthermore, the variance and the mean data can also be used to generate a beam-hardening correction curve that qualitatively improves a conventionally reconstructed tomogram. We demonstrate this in various simulation studies and discuss the broader implications.
Carl (Qiheng) Yang (Tue,) studied this question.