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The subject of interest is the superresolution of atmospheric-turbulence-degraded, short-exposure imagery, where superresolution refers to the removal of blur caused by a diffraction-limited optical system along with recovery of some object spatial-frequency components outside the optical passband. Photon-limited space object images are of particular interest. Two strategies based on multiple exposures are explored. The first is known as deconvolution from wave-front sensing, where estimates of the optical transfer function (OTF) associated with each exposure are derived from wave-front-sensor data. New multiframe superresolution algorithms are presented that are based on Bayesian maximum a posteriori and maximum-likelihood formulations. The second strategy is known as blind deconvolution, in which the OTF associated with each frame is unknown and must be estimated. A new multiframe blind deconvolution algorithm is presented that is based on a Bayesian maximum-likelihood formulation with strict constraints incorporated by using nonlinear reparameterizations. Quantitative simulation of imaging through atmospheric turbulence and wave-front sensing are used to demonstrate the superresolution performance of the algorithms.