Spatial resolution and image noise are two aspects of image quality of an x-ray computed tomography (CT) system, and are determined by the x-ray source, the detector, and mathematical operations for image reconstruction. In CT scanners with flat panel detectors, there is cross-talk (signal leakage) between detector pixels. The contribution of the cross-talk to spatial resolution and noise in reconstructed images has not been adequately modeled. Previously, we estimated cross-talk from autocovariance measurements in air, and modeled the impact of cross-talk on spatial resolution. We have extended that work to calculate the impact of cross-talk on signal-to-noise ratio in radiographs and to reconstructed image noise. We modeled the spatial resolution and noise of a CT scanner that uses a flat-panel detector with 0.2 mm pixels and a gadolinium oxysulfide scintillator, and a 450 kVp, dual-focus x-ray tube. Our noise model agrees with measurements from experimental data and simulations to within 10%. We show that cross-talk in flat panel detectors can reduce resolution by over 30%, reduce noise by approximately a factor of two, and introduce correlation in the noise, and therefore, cannot be disregarded when assessing CT image quality.