Robust Phase Retrieval with Complexity-Guidance for Coherent X-Ray Imaging

Abstract

Reconstruction of a stable and reliable solution from noisy and incomplete Fourier intensity data is a challenging problem for iterative phase retrieval algorithms. The typical methodology employed in the coherent X-ray imaging (CXI) literature involves thousands of iterations of well-known phase retrieval algorithms, e.g., hybrid input-output (HIO) or relaxed averaged alternating reflections (RAAR), that are concluded with a smaller number of error reduction (ER) iterations. Since the single run of this methodology may not provide a reliable solution, hundreds of trial solutions are first obtained by initializing the phase retrieval algorithm with independent random guesses. The resulting trial solutions are then averaged with appropriate phase adjustment, and resolution of the averaged reconstruction is assessed by plotting the phase retrieval transfer function (PRTF). In this work, we examine this commonly used RAAR-ER methodology from the perspective of the complexity parameter introduced by us in recent years. It is observed that the single run of the RAAR-ER algorithm provides a solution with undesirable grainy artifacts that persist to some extent even after averaging the multiple trial solutions. The grainy features are spurious in the sense that they are smaller in size compared to the resolution predicted by the PRTF curve. This inconsistency can be addressed by a novel methodology that we refer to as complexity-guided RAAR (CG-RAAR). The methodology is demonstrated with simulations and experimental data sets from the CXIDB database. In addition to providing consistent solution, CG-RAAR is also observed to require reduced number of independent trials for averaging.