Material decomposition using a singular value decomposition method

The development of photon counting detectors enables us to decompose materials in x-ray CT images. The photon counting detection can measure a linear attenuation coefficient of a given energy range, thereby contributing to the material decomposition or identification. In this detection, measured photon counts were affected by statistical noise, making it difficult to obtain accurate measurements of material concentration. To calculate this concentration ratio the principal component analysis is sometimes used, although the results are much affected by the noise included in the measured data. In this paper we evaluate the performance of the singular value decomposition (SVD) method for the purpose of material decomposition using the numerical simulation phantom and Monte Carlo simulation. The materials used were water, calcium, Au-colloid, and gadolinium solution. The results of simulations showed that the accuracy strongly depended on the setting of energy windows and the energy resolution of the detector.