A Non-Iterative Crosswords-Inspired Approach to the Recovery of 2-D Discrete Signals from Phaseless Fourier Transform Data

We propose an innovative approach to the phase retrieval of 2-D discrete complex signals. The solution strategy profitably exploits some fundamental results available for the phase retrieval of one-dimensional discrete signals by following a simple yet effective philosophy resembling the solution of crossword puzzles. The resulting procedure is completely deterministic and allows identifying all the solutions of the problem by using just the spectral amplitude data, knowledge of the support of the source, and a few additional information. As a distinguishing characteristic, it does not exploit neither global-optimization algorithms nor iterative techniques. Numerical examples witnessing the interest of the proposed ideas are given for antenna applications.