Abstract

In a variety of contexts, it is desirable to reconstruct a sequence from partial Fourier domain information. As a consequence, considerable attention has been paid to, and some significant results have been developed in, this area. For example, it has been established [1,2] that under very mild restrictions a finite extent one-dimensional (1-D) or multi-dimensional (M-D) sequence is uniquely specified to within a scale factor by its Fourier transform (FT) phase, and algorithms for implementing the reconstruction have been developed. It is well known that in contrast, the FT magnitude does not uniquely specify a 1-D sequence. Even for M-D sequences, the FT magnitude specifies a sequence only to within a translation and a central symmetry [2], and reconstruction algorithms developed so far have been successful [2] for only a very restricted class of M-D sequences.

© 1983 Optical Society of America