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Photon-counting detector technology has enabled the first experimental investigations of energy-resolved computed tomography (CT) imaging and the potential use for K-edge imaging. However, limitations in regards to detecter technology have been imposing a limit to effective count rates. As a consequence, this has resulted in high noise levels in the obtained images given scan time limitations in CT imaging applications. It has been well recognized in the area of low-dose imaging with conventional CT that iterative image reconstruction provides a superior signal to noise ratio compared to traditional filtered backprojection techniques. Furthermore, iterative reconstruction methods also allow for incorporation of a roughness penalty function in order to make a trade-off between noise and spatial resolution in the reconstructed images. In this work, we investigate statistically-principled iterative image reconstruction …