Multidimensional signal reconstruction from phase or magnitude

This paper reviews some recent results concerning the uniqueness of a multi-dimensional (m-D) sequence in terms of the phase or magnitude of its Fourier transform. Specifically, some conditions are presented under which an m-D sequence is uniquely specified by its phase or magnitude. In addition, an iterative algorithm is described which has been proposed for reconstructing a sequence from its phase or magnitude. Several examples of phase-only and magnitude-only reconstruction are also presented.