The presence of atmospheric turbulence degrades the angular resolution attainable using conventional photographic methods with an astronomical telescope. Near diffraction-limit resolution has been obtained using statistical measurements from short exposure photographs by Labeyrie. A signal processing method for the A posteriori restoration of atmospherically degraded images is developed. The emphasis is on near "optimal" processing of the measurements so that the images are restored without enhancing the unwanted noise effects. Short exposure images are used to "freeze" the motion caused by atmospheric turbulence. Multiframe imagery is used to obtain first and second order statistics of the degraded images. The integral equations relating the measured statistics to the underlying object and atmospheric characteristics are derived. A multi-step process is developed for solving these integral equations. An estimate of the Cartesian product of the object with itself is obtained from the second order statistics using Fourier methods. An estimate of the object is then derived from an eigen expansion of the Cartesian product. This estimate is augmented by an estimate from the first order statistics. The performance of this restoration method is illustrated by simulation results.
James W. Sherman,
"A Posteriori Restoration Of Atmospherically Degraded Images Using Multiframe Imagery", Proc. SPIE 0074, Image Processing, (9 July 1976); doi: 10.1117/12.954727; https://doi.org/10.1117/12.954727