Context: Spectral Computed Tomography (SPCT) acquires energy-resolved projections that can be used to evaluate the concentrations of the different materials of an object. This can be achieved by decomposing the projection images in a material basis, in a first step, followed by a standard tomographic reconstruction step. However, material decomposition is a challenging non-linear ill-posed inverse problem, which is very sensitive to the photonic noise corrupting the data.

Methods: In this paper, material decomposition is solved in a variational framework. We investigate two fidelity terms: a weighted least squares (WLS) term adapted to Gaussian noise and the Kullback–Leibler (KL) distance adapted to Poisson Noise. The decomposition problem is then solved iteratively by a regularized Gauss–Newton algorithm.

Results: Simulations are performed in a numerical mouse phantom and the decompositions show that KL outperforms WLS for low numbers of photons, i.e., for high photonic noise.

Conclusion: In this work, a new method for material decomposition in SPCT is presented. It is based on the KL distance to take into account the noise statistics. This new method could be of particular interest when low-dose acquisitions are performed.