Abstract

The problem of restoring a constant image distorted by a system of random time-varying impulse response is discussed. The restoration is based on the observed time-varying distorted image during a finite period of time T. Three methods are considered. Restorations based on the average image is considered first. If the observation time T is finite, the system noise remains to play a role. This results in a restoration problem with object-dependent noise. Second, restoration based on the averaged spatial correlation of the image will be introduced. For finite T the result is an image restoration problem which we could not solve. Third, restoration based on a finite number of image frames will be examined in detail. We use an iterative method based on the minimum-variance unbiased estimation. When the frames are uncorrelated, we obtain the result based on using the average image as a statistic. When the frames are correlated but space–time separable, a Karhunen-Loève transformation that decorrelates the frames is used to reduce the computations. Using an example, we show how the restoration error drops as more frames are included. The higher the interframe correlation, the more reduction of restoration error is obtained by using the frame data, compared with the error of restoration based on frame averaging.

© 1985 Optical Society of America