Unique reconstruction of a band-limited multidimensional signal from its phase or magnitude

The mathematical problem of unique recovery of a band-limited multidimensional signal from its phase or its magnitude is considered. Specifically, we show that any irreducible band-limited function f(s1, …, sn), si∈C, i = 1, …, n is uniquely determined, except for trivial associates, from (1) the phase of f(x1, …, xn), xi∈ ℛ, i = 1, …, n, if not all the zeros of f(s1, …, sn) occur in conjugate pairs; or (2) the magnitude of f(x1, …, xn), xi∈ ℛ, i = …, n.