Non-linear regularized decomposition of spectral x-ray projection images

Spectral computed tomography (CT) exploits measurements from x-rays with different energies to obtain the 3D description of the patient in a material basis. It requires to solve two subproblems, namely the material decomposition and the tomographic reconstruction problems, either sequentially or jointly. In this work, we address the material decomposition problem, which an ill-posed non-linear problem. Our main contribution is to introduce a material-dependent spatial regularization scheme. The problem is solved iteratively using the Gauss-Newton’s method. The framework is validated on numerical experiments of a thorax phantom made of soft tissue, bone and gadolinium scanned with a 90 kV source and a 3-bin photon counting detector.