ABSTRACT
Spectral Computed Tomography (CT) aims at measuring the energy-resolved three-dimensional (3D) distribution of the x-ray attenuation coefficients of a scanned object. It is not only a challenge for the detector hardware: taking advantage of the measured energy-resolved x-ray projections also requires to solve a complex non-linear inverse problem. Most solutions to this inverse problem use the model of Alvarez and Macovski [4], which decomposes the x-ray attenuation coefficient of all materials of the object into the sum of a few energy-dependent but material-independent functions weighted by material-specific coefficients. From this model, solving the inverse problem of spectral CT is twofold: decomposition into materials and tomographic reconstruction. This chapter reviews the state-of-the-art of spectral CT inversion methods. It includes image-based methods, which start with tomographic reconstruction and then apply material decomposition; projection-based methods, where material decomposition is performed before tomographic reconstruction; and one-step inversion, where the two problems are solved simultaneously. The pros and cons of each solution are summarized, and we conclude with the challenges that lie ahead.
