Greedy phase retrieval with reference points and bounded sparsity

Abstract

The phase retrieval problem of recovering a data vector from the squared magnitude of its Fourier transform in general can not be solved uniquely, since the magnitude of the Fourier transform is invariant to a global phase shift, cyclic spatial shift and the conjugate reversal of the signal. We discuss a method of introducing reference points in the signal to resolve aforementioned ambiguities. After specifying requirements for these reference points we present a modification of the GESPAR algorithm to solve the obtained problem.