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 band-limits 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.