Free log-likelihood as an unbiased metric for coherent diffraction imaging

Area of Science:

• X-ray science
• Diffraction imaging
• Computational imaging

Background:

• Coherent Diffraction Imaging (CDI) reconstructs objects from diffraction patterns, but phase recovery is challenged by unknown object support.
• Uncertainty in object support leads to over-fitting and hinders objective evaluation of CDI solutions.
• Existing methods lack an unbiased metric for validating reconstructions across different sample types.

Purpose of the Study:

• To introduce a novel, unbiased metric for evaluating the validity of Coherent Diffraction Imaging solutions.
• To develop a method for improving object support estimation using eigen-decomposition of solution sets.
• To demonstrate the applicability of the proposed method for diverse materials and advanced X-ray sources.

Main Methods:

• A 'free' log-likelihood indicator is proposed, utilizing a small percentage of masked data points during reconstruction.
• This indicator provides an unbiased evaluation metric, independent of the specific sample characteristics.
• Eigen-decomposition of multiple solutions is employed to refine the estimate of the true object.

Main Results:

• The free log-likelihood indicator effectively validates CDI reconstructions without prior knowledge of object support.
• Eigen-decomposition analysis yields improved estimates of the object's true form from a set of solutions.
• Successful analysis was demonstrated on both test pattern datasets and experimental diffraction data from cyanobacteria.

Conclusions:

• The proposed method offers an unbiased approach for validating CDI reconstructions across hard condensed and biological materials.
• This technique is particularly valuable for unsupervised data evaluation in high-throughput experiments at 4th generation synchrotrons and X-ray free-electron lasers.
• The free log-likelihood indicator and eigen-decomposition analysis enhance the reliability and accuracy of CDI.