Phase retrieval from local measurements in two dimensions

The phase retrieval problem has appeared in a multitude of applications for decades. While ad hoc solutions have existed since the early 1970s, recent developments have provided algorithms that offer promising theoretical guarantees under increasingly realistic assumptions. Motivated by ptychographic imaging, we generalize a recent result on phase retrieval of a one dimensional objective vector x ∈ ℂd to recover a two dimensional sample Q ∈ ℂd x d from phaseless measurements, using a tensor product formulation to extend the previous work.