Robust Phaseless Imaging via Reverse Kullback-Leibler Divergence—Part 1: Reconstruction Methods

Robustness to noise and outliers is desirable in phase retrieval algorithms for many imaging and signal-processing applications. In Part 1 of this two-part article, we develop novel robust phase retrieval algorithms based on minimizing reverse Kullback–Leibler divergence (RKLD) within the Wirtinger flow (WF) framework. We use RKLD over intensity-only measurements in two distinct ways: 1) to design a novel initial estimate based on minimum distortion design of spectral estimates and 2) as a loss function for iterative refinement based on WF. The RKLD-based loss function, independent of the noise distribution of the measurements, reduces the impact of contamination by the logarithmic processing of the measurements. We present three algorithms based on RKLD minimization, including two with sample truncation schemes to enhance the robustness to significant contamination. Our numerical simulation results, using synthetic coded diffraction pattern (CDP) measurements and a real optical imaging dataset, highlight the superiority of the truncation-free RKLD-based WF algorithm compared with the state-of-the-art algorithms with respect to convergence speed, sample efficiency, and robustness to noise and outliers. In Part 2, we present a quantitative analysis of the robustness of the RKLD-minimization-based algorithms and the performance evaluation of the truncation-based algorithms using real and simulated data.