Modern computed tomography (CT) uses detector arrays consisting of large numbers of photodiodes with scintil- lator crystals. The number of pixels in the array can play an important role in system performance. Considerable research has been performed on signal detection in flat backgrounds under various conditions, but little has been done with complex, random backgrounds in CT; our work investigates in particular the effect of the number of detector elements on signal detection by a channelized Hotelling observer in a complex background. For this project, a simulated three-dimensional phantom is generated with its attenuation equal to that of water. The phantom contains a smaller central section with random variations to simulate random anatomical structures. Cone-beam projections of the phantom are acquired at different angles and used to calculate the covariance matrix of the raw projection data. Laguerre-Gauss channels are used to reduce the dimensionality of each 2D projection and hence the size of the covariance matrix, but the covariance is still a function of two projection angles. A strong cross-channel correlation is observed as a function of the difference between the angles. A signal with known location and size is used, and the performance of the observer is calculated from the channel outputs at multiple projection angles. A contrast-detail diagram is computed for different variables such as signal size, number of incident x-ray photons, pixel size, etc. At a fixed observer signal-to-noise ratio (SNR), the contrast required to detect a signal increases dramatically as the signal size decreases.