Robust Phaseless Imaging via Reverse Kullback-Leibler Divergence—Part 2: Robustness Analysis and Performance Evaluation

Phaseless imaging refers to reconstructing an image from its intensity-only measurements, a task complicated by noise and outliers in real-world applications. In Part 1, we introduced the reverse Kullback-Leibler divergence (RKLD) as a loss function for phase retrieval in the presence of noise and outliers. Coupled with an RKLD-based spectral initialization technique, we presented three-phase retrieval algorithms using the RKLD-based loss function within the Wirtinger flow (WF) framework. In Part 2, we present a theoretical analysis of the robustness of the RKLD-based algorithms with respect to noise and outliers and compare it with the robustness offered by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{{2}}$ </tex-math></inline-formula> and Poisson loss-based algorithms. Specifically, we study the sensitivity of the RKLD-based loss function with respect to the magnitude of outliers and show that it is bounded while the sensitivity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{{2}}$ </tex-math></inline-formula> and Poisson-based loss functions are unbounded. Additionally, we present extensive numerical experiments using both simulated and real data to demonstrate the performance of our truncation-based algorithms. The results show the advantages of our algorithms in terms of sample efficiency and robustness with respect to noise and outliers over truncation-based state-of-the-art algorithms.