This paper describes a rather broad class of iterative signal restoration
techniques which can be applied to remove the effects of many different
types of distortions. These techniques also allow for the incorporation
of prior knowledge of the signal in terms of the specification of
a constraint operator. Conditions for convergence of the iteration
under various combinations of distortions and constraints are explored.
Particular attention is given to the use of iterative restoration
techniques for constrained deconvolution, when the distortion bandlimits
the signal and spectral extrapolation must be performed. It is shown
that by predistorting the signal (and later removing this predistortion)
it is possible to achieve spectral extrapolation, to broaden the
class of signals for which these algorithms achieve convergence,
and to improve their performance in the presence of broad-band noise.
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