Density Estimation in X-ray Computed Tomography using the Alvarez-Macovski Model

We introduce a method to extract density information from an x-ray computed tomography (XCT) volume that is more accurate than simply assuming density is proportional to CT number. XCT is a versatile tool for analysis, however, for lab-based XCT machines that employ polychromatic x-rays, it is difficult to extract anything more than the crudest quantitative data from the sample. Reconstructed tomograms values are, in theory, the x-ray attenuation coefficients of the material. However, due to the polychromatic nature of the beam, and effects such as beam hardening, such an interpretation of real data is rarely feasible. The Alvarez-Macovski (AM) equation, which is used in quantitative XCT reconstruction algorithms, provides a model of x-ray attenuation. We use the AM equation to extract quantitative information from conventionally reconstructed tomograms, provided it is not too severely affected by beam-hardening artefacts. In essence, we assume that the tomogram values are proportional to the attenuation coefficients of the AM equation at a mean x-ray energy. Then, given a calibration scan which contains enough materials, we can solve the AM equation for the unknown coefficients and exponents. We then apply it to tomograms of objects with similar shape and material composition. The quantitative data extracted thus provides a more accurate estimate of both per-material density and bulk density.