Real space in cryo-EM: the future is local

Cryo-EM images have extremely low signal-to-noise levels because biological macromolecules are highly radiation-sensitive, requiring low-dose imaging, and because the molecules are poor in contrast. Confident recovery of the signal requires the averaging of many images, the iterative optimization of parameters and the introduction of much prior information. Poor parameter estimates, overfitting and variations in signal strength and resolution across the resulting reconstructions remain frequent issues. Because biological samples are real-space phenomena, exhibiting local variations, real-space measures can be both more reliable and more appropriate than Fourier-space measures. Real-space measures can be calculated separately over each differing region of an image or volume. Real-space filters can be applied according to the local need. Powerful prior information, not available in Fourier space, can be introduced in real space. Priors can be applied in real space in ways that Fourier space precludes. The treatment of biological phenomena remains highly dependent on spatial frequency, however, which would normally be handled in Fourier space. We believe that measures and filters based around real-space operations on extracted frequency bands, i.e. a series of band-pass filtered real-space volumes, and over real-space densities of striding (sequentially increasing or decreasing) resolution through Fourier space are the best way to address this and will perform better than global Fourier-space-based approaches. Future developments in image processing within the field are generally expected to be based on a mixture of both rationally designed and deep-learning approaches, and to incorporate novel prior information from developments such as AlphaFold. Regardless of approach, it is clear that `locality', through real-space measures, filters and processing, will become central to image processing.