This work proposes a dedicated statistical algorithm to perform a direct reconstruction of material-decomposed images from data\nacquired with photon-counting detectors (PCDs) in computed tomography. It is based on local approximations (surrogates) of the\nnegative logarithmic Poisson probability function. Exploiting the convexity of this function allows for parallel updates of all image\npixels. Parallel updates can compensate for the rather slow convergence that is intrinsic to statistical algorithms.We investigate the\naccuracy of the algorithm for ideal photon-counting detectors. Complementarily, we apply the algorithm to simulation data of a\nrealistic PCD with its spectral resolution limited by K-escape, charge sharing, and pulse-pileup. For data from both an ideal and\nrealistic PCD, the proposed algorithm is able to correct beam-hardening artifacts and quantitatively determine the material fractions\nof the chosen basis materials. Via regularization we were able to achieve a reduction of image noise for the realistic PCD that is up\nto 90% lower compared to material images form a linear, image-based material decomposition using FBP images. Additionally, we\nfind a dependence of the algorithms convergence speed on the threshold selection within the PCD.
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