  Quantifying material mass and electron density from computed tomography (CT)
reconstructions can be highly valuable in certain medical practices, such as
radiation therapy planning. However, uniquely parameterising the X-ray
attenuation in terms of mass or electron density is an ill-posed problem when a
single polyenergetic source is used with a spectrally indiscriminate detector.
Existing approaches to single source polyenergetic modelling often impose
consistency with a physical model, such as water--bone or
photoelectric--Compton decompositions, which will either require detailed prior
segmentation or restrictive energy dependencies, and may require further
calibration to the quantity of interest. In this work, we introduce a data
centric approach to fitting the attenuation with piecewise-linear functions
directly to mass or electron density, and present a segmentation-free
statistical reconstruction algorithm for exploiting it, with the same order of
complexity as other iterative methods. We show how this allows both higher
accuracy in attenuation modelling, and demonstrate its superior quantitative
imaging, with numerical chest and metal implant data, and validate it with real
cone-beam CT measurements.
