Sparsity-based Phase Retrieval from Diffractive Optical Imaging

Abstract

Phase retrieval (PR) is an inverse problem that consists on estimating a signal from phaseless measurements. Recent algorithms have been developed to solve this problem assuming that the signal is sparse on some representation base. On the other hand, in the state-of-the-art has been studied theoretically this problem under a setup that collects coded diffraction patterns at the far field. However, employed coding elements are inadmissible because they allow increments on the power of the signal in the modulation process. Further, the near and middle fields setup remain without any theoretical guarantees of signal recovery. Therefore, this paper provides exact recovery guarantees on any optical field from sparsity-based coded phaseless measurements that meet an admissible modulation. Numerical results show that the proposed coding elements are able to solve sparsity-based PR at any optical field under an admissible modulation. In fact, the results show the types of admissible coding elements that best estimate the support.