A new phase consistency criterion and its application in electron crystallography

In this work, we present the principles and potential advantages of a methodology to assess Fourier components in terms of phase consistency. We define a new phase consistency criterion among sets of spatially translated images based upon a novel conception of the spatial shift property of the Fourier transform. The article shows how this criterion can be used in the alignment stage of the 3D reconstruction process with a two-fold objective: Assessment of the frequency components and robustness in the alignment. In that sense, the article shows and analyzes the results obtained from the application of the new index of quality in the context of projection image alignment. We have focussed our attention on the electron crystallography field, by applying such a phase consistency definition over image reflections. The results that have been obtained show that the new phase-consistency definition may complement the traditional SNR-based index of quality (commonly known as IQ) of reflections. As a consequence, the reliability of the alignment may be improved by discarding those reflections judged as non-reliable according to the phase-consistency criterion.