We introduce a modified Backus-Gilbert technique for restoring an image that has been distorted by a linear system whose impulse response function is itself random, and in the presence of detection noise. The restoration is based on a weighted superposition of a small number of shifted versions of the distorted image. Optimum weights are determined to minimize a measure of the average width of the impulse response functions of the overall system and the noise variance.
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Ward et al. (1987) studied this question.