Noise reduction in adaptive-optics imagery with the use of support constraints

The use of support constraints for noise reduction in images obtained with telescopes that use adaptive optics for atmospheric correction is discussed. Noise covariances are derived for these type of data, including the effects of photon noise and CCD read noise. The effectiveness of support constraints in achieving noise reduction is discussed in terms of these noise properties and in terms of the types of algorithms used to enforce the support constraint. Both a convex-projections and a cost-function minimization algorithm are used to enforce the support constraints, and it is shown with the use of computer simulations and field data that the cost-function algorithm results in artifacts in the reconstructions. The convex-projections algorithms produced mean-square-error decreases in the image domain of approximately 10% for high light levels but essentially no error decreases for low light levels. We emphasize images that are well resolved by the telescope and adaptive-optics system.