[en] We consider noise in computed tomography images that are reconstructed using the classical direct fan-beam filtered backprojection algorithm, from both full- and short-scan data. A new, accurate method for computing image covariance is presented. The utility of the new covariance method is demonstrated by its application to the implementation of a channelized Hotelling observer for a lesion detection task. Results from the new covariance method and its application to the channelized Hotelling observer are compared with results from Monte Carlo simulations. In addition, the impact of a bowtie filter and x-ray tube current modulation on reconstruction noise and lesion detectability are explored for full-scan reconstruction