This paper deals with the long-standing problem of reconstructing an optical object of known finite spatial extent from an image that is a noisy low-pass-filtered version of the object. The development of a number of iterative reconstruction algorithms in recent years has created a resurgence of interest in this topic. We consider several reconstruction algorithms from a point of view that illuminates their performance in the presence of noise. We also introduce a new iterative reconstruction algorithm and compare its performance with that of an earlier algorithm proposed by Gerchberg.
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