Restoration of images degraded by atmospheric turbulence and detection noise

The restoration of images blurred by atmospheric turbulence and contaminated by additive-signal-independent noise is investigated. A series of noisy short-exposure images and the a priori knowledge of the time-averaged autocorrelation function of the optical transfer function are assumed to be known. Three kinds of filter are discussed. These are based on the speckle interferometry technique, the Wiener criterion, and an ad hoc scheme. The Wiener estimates have the advantage that all the observations are considered simultaneously, but unfortunately the estimates require more knowledge about the optical transfer function than is available. Thus the ad hoc scheme is developed so that the least-squares estimate for each observation is first obtained. Then the Fourier modulus of the unknown is obtained by time averaging a function of these estimates. The experimental results verify the theoretical expectation that this ad hoc filter should outperform that based on the speckle interferometry technique in that the additive-noise effects are suppressed and the image quality is improved significantly.