On the Processing of a Motion-Blurred Image

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Abstract
We construct stochastic process models for test-patterns and image degradation in the context of image processing. Using these models, information-theoretic bounds are obtained for the amount of detail that can be removed from a motion-blurred image corrupted by white noise. It is shown that the bounds are attained by estimators based on smoothed Fourier inversion, provided the two smoothing parameters are chosen correctly. In this sense, smoothed Fourier inversion permits optimal restoration of a motion-blurred image. It is also shown that details up to one-third the width of a motion blur can be slightly enhanced by simply blurring the image again.

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