# Measuring Identification and Quantification Errors in Spectral CT Material Decomposition
## 1 Introduction  
Spectral (multi-energy) computed tomography is an extension of dual-energy computed tomography (DECT) or single energy CT. In spectral CT, a single broad X-ray spectrum is compartmental into separate energy bins by photon counting detectors to extract energyinformation to improve contrast discrimination and material decomposition [1]. In recent years, spectral CT with single photon energy sensitive detection systems has offered the potential for a range of CT applications, such as spectral imaging of vulnerable atherosclerotic plaque [2; 3], discrimination between iodine and barium [4; 5], soft tissue quantification [6; 7], beam hardening effects and metal artefact reduction in orthopedic applications [8], quantitative imaging of excised osteoarthritis cartilage [9], and K-edge imaging of high-Z (atomic number) biomedical nanoparticles [10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. The potential to use spectral information for decomposing the linear attenuation coefficient into two or more basis for material discrimination (also called material decomposition MD) was proposed by [PERSON] and [PERSON] in 1976 [20]. They analyzed the material decomposition in the projection image domain (pre-reconstruction). Later in 1977, [PERSON] [21] successfully demonstrated the dual energy material decomposition method in the reconstruction image domain (post-reconstruction). However, both of these early methods performed decomposition only into photoelectric and Compton components and assumed an absence of K-edges within the energy bins which is not always the case. This method is only valid for low atomic number materials (Z \(<\) 20) whose K-edge is not detectable in the human diagnostic energy range. Elements with more than 40 protons in the nucleus can be referred to as heavy atoms or high Z materials. Atoms heavier than this feature a sharp discontinuity in their X-ray attenuation profile, caused by the binding energy of the innermost (K) shell electrons. Only photons with energies higher than the binding energy have the possibility to knock out the K-shell electrons. Accordingly, photons with energies just above the K-edge are attenuated more than just below. Spectral CT imaging using K-edge energies was first investigated by [PERSON] and [PERSON] in 1977 [22]. Subsequently, the decomposition of the high-Z materials has been evaluated in projection space [15; 23; 24] and in image space [5; 6; 25]. The objective of both projection or image based decomposition is to produce basis images with an optimum signal to noise ratio [26]. The main advantage of spectral decomposition is that it allows identification and quantification of multiple high-Z elements in the same scan with high sensitivity and specificity. However, the amount of spectral information can be affected by various factors such as the limited number of independent energy thresholds, incorrect arrangement of the energy bins and their separation size [26], charge sharing [27], charge trapping [28; 29; 30], K-fluorescence X-rays from high-Z detectors [31], scatter X-rays, semiconductor detector inhomogenities, and pulse pileup [32; 33] in the photon counting detectors. These effects are intrinsic to detector properties and some of them can be compensated by flat field correction. However, it is the energy-dependent effects that cannot be corrected by the flat-fielding process, thereby contributing to errors in identification of materials. Despite considerable development in material decomposition algorithms made over the last few years [6; 24; 33; 34], almost no work has been done on the quantitative assessment of MD images. Quality of material images is typically assessed through residual images from simulated or phantom data [35; 36; 37] and their SNR [36]. These techniques give a view of the average quantitative and qualitative image quality, but not an accurate classification on the voxel scale. Thus it is important to know the degree of confidence which can be placed on the identity and quantity of any material provided by spectral CT.