Abstract
Reconstruction of a stable and reliable solution from noisy incomplete
Fourier intensity data recorded in a coherent X-ray imaging (CXI) experiment is
a challenging problem. The Relaxed Averaged Alternating Reflections (RAAR)
algorithm that is concluded with a number of Error Reduction (ER) iterations is
a popular choice. The RAAR-ER algorithm is usually employed for several
hundreds of times starting with independent random guesses to obtain trial
solutions that are then averaged to obtain the phase retrieval transfer
function (PRTF). In this paper, we examine the phase retrieval solution
obtained using the RAAR-ER methodology from perspective of the complexity
parameter that was introduced by us in recent works. We observe that a single
run of the RAAR-ER algorithm produces a solution with higher complexity
compared to what is expected based on the complexity parameter as manifested by
spurious high frequency grainy artifacts in the solution that do not seem to go
away completely even after a number of trial solutions are averaged. We then
describe a CG-RAAR (Complexity Guided RAAR) phase retrieval method that can
effectively address this inconsistency problem and provides artifact-free
solutions. The CG-RAAR methodology is first illustrated with simulated
unblocked noisy Fourier intensity data and later applied to centrally-blocked
noisy cyanobacterium data which is available from the CXIDB database. Our
simulation and experimental results using CG-RAAR suggest two important
improvements over the popular RAAR-ER algorithm. The CG-RAAR solutions after
the averaging procedure is more reliable in the sense that it contains smallest
features consistent with the resolution estimated by the PRTF curve. Secondly,
since the single run of the CG-RAAR solution does not have grainy artifacts,
the number of trial solutions needed for the averaging process is reduced.
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