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We present a statistically principled sinogram smoothing approach for X-ray computed tomography (CT) with the intent of reducing noise-induced streak artifacts. Noise-induced streak artifacts arise in CT when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines. Attempts to reduce these artifacts have focused on the use of adaptive filters that attempt to tailor the degree of smoothing to the local noise levels in the measurements. While these approaches involve loose consideration of the measurement statistics to determine smoothing levels, they are not explicitly statistical methods in that they do not explicitly model the statistical distribution of the measurement data. In this work, we present an explicitly statistical approach to sinogram smoothing in the presence of photon-starved measurements. It is an extension of a nonparametric sinogram smoothing approach using penalized Poisson likelihood functions that we have previously developed for emission tomography. Because the approach explicitly models the data statistics it is naturally adaptive - it will smooth more variable measurements more heavily than it does less variable measurements. We find that it significantly reduces streak artifacts and noise levels without comprising image resolution.