From spectral decomposition through SVD to quantitative description of monochromatic CT images: a phantom study

In this work, we applied the singular value decomposition (SVD) method to a set of monochromatic images to extract the dominant physical contributions to image formation. We showed that the first two principal components can be related to an arbitrary pair of basis material in mathematically enclosed expression. The later principal components are assumed to carry mostly sub-leading image formation effects, noise, and reconstruction artifact contribution. The proof of concept is shown on numerical (linear) images and later confirmed on physical spectral CT phantom images obtained with monochromatic x-ray radiation at Elettra synchrotron in Trieste, Italy. Following material decomposition, we also performed a quantitative description of tissue-equivalent phantom materials in terms of material density and effective atomic number.