Reduction of artifacts associated with missing data in coherent diffractive imaging.

Area of Science:

• Coherent diffractive imaging
• Phase retrieval
• Image reconstruction

Background:

• Coherent diffractive imaging (CDI) experiments frequently yield incomplete datasets due to experimental limitations like beamstops or detector gaps.
• Incoherent data regions, particularly the 'missing wedge' in tomography, introduce significant artifacts in 3D reconstructions.
• Existing phase retrieval methods struggle with these data deficiencies, limiting the quality of reconstructed images.

Purpose of the Study:

• To develop practical and effective algorithms for mitigating reconstruction artifacts in CDI caused by incomplete datasets.
• To restore uniqueness to the phase retrieval problem by incorporating prior information about data quality.
• To improve the accuracy and reduce oscillations in reconstructed images from limited or corrupted data.

Main Methods:

• Two algorithms were developed to address the missing data problem in phase retrieval.
• The first algorithm uses an estimated phase for pre- and post-processing to refine reconstructions.
• The second algorithm simultaneously minimizes total variation and recovers the phase, directly tackling data incompleteness.

Main Results:

• The proposed algorithms effectively mitigate reconstruction artifacts arising from incomplete datasets in CDI.
• Minimum total variation regularization was shown to reduce oscillations and improve the solution's uniqueness.
• Successful demonstration of the algorithms using numerical simulations and a large, three-dimensional experimental dataset.

Conclusions:

• The developed algorithms provide practical solutions for handling incomplete data in coherent diffractive imaging.
• Incorporating minimum total variation is a powerful strategy to enhance phase retrieval from limited datasets.
• These methods significantly improve the quality of 3D reconstructions in the presence of experimental data gaps.