Restoration of atmospherically degraded images is limited most fundamentally by the photon noise inherent in any detected image. After presenting a general model for photon-limited images, we derive the form of the linear, space invariant filter which restores the image with minimum mean-squared error. Measures of the restorable bandwidth and image quality are developed. The theory is applied to the case of images degraded by atmospheric turbulence, both with and without perfect tilt removal. The relationship between the number of detected photoevents and the restorability of the degraded images is quantified.