Investigation of the polynomial approach for material decomposition in spectral X-ray tomography using an energy-resolved detector

Recent advances in the domain of energy-resolved semiconductor detectors stimulate research in X-ray computed tomography (CT). However, the imperfections of these detectors induce errors that should be considered for further applications. Charge sharing and pile-up effects due to high photon fluxes can degrade image quality or yield wrong material identification. Basis component decomposition provides separate images of principal components, based on the energy related information acquired in each energy bin. The object is typically either decomposed in photoelectric and Compton physical effects or in basis materials functions. This work presents a simulation study taking into account the properties of an energy-resolved CdTe detector with flexible energy thresholds in the context of materials decomposition CT. We consider the effects of a first order pile-up model with triangular pulses of a non-paralyzable detector and a realistic response matrix. We address the problem of quantifying mineral content in bone based on a polynomial approach for material decomposition in the case of two and three energy bins. The basis component line integrals are parameterized directly in the projection domain and a conventional filtered back-projection reconstruction is performed to obtain the material component images. We use figures of merit such as noise and bias to select the optimal thresholds and quantify the mineral content in bone. The results obtained with an energy resolved detector for two and three energy bins are compared with the ones obtained for the dual-kVp technique using an integrating-mode detector with filters and voltages optimized for bone densitometry.