Sufficient Support Information to Ensure a Unique Solution to the Phase Problem

It is evident that the support of a function can have a strong influence upon one’s ability to uniquely reconstruct that function from its autocorrelation, both in terms of solution multiplicity, and in the convergence of certain reconstruction algorithms. Greenaway [1] first demonstrated that the number of solutions to the one—dimensional phase problem is reduced if an internal region of the function in question is known to be zero. This is a strong statement, because generally the one-dimensional phase problem is intractable due to large numbers of non-equivalent solutions. More recently Sault [2] has shown that one can always ensure solution uniqueness for discrete functions if the internal zero region is specified and somewhat more complex.