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

Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object, which prevents an unambiguous metric evaluation of solutions. We propose to use a 'free' log-likelihood indicator, where a small percentage of points are masked from the reconstruction algorithms, as an unbiased metric to evaluate the validity of proposed solutions, independent of the sample studied. We also show how a set of solutions can be analysed through an eigen-decomposition to yield a better estimate of the real object. Example analysis on experimental data is presented both for a test pattern dataset, and the diffraction pattern from a live cyanobacteria cell. The method allows the validation of reconstructions on a wide range of materials (hard condensed, biological,..), and should be particularly relevant for 4th generation synchrotrons and X-ray free electron lasers, where large, high-throughput datasets require a method for unsupervised data evaluation.