The Phantom in the Noise and Validation of 3D EM Reconstructions

Single particle reconstructions derived from electron micrographs yield increasing detail of biological molecules and assemblies. However, it is well-known that alignment of pure noise images against a reference can recover that reference on reconstruction [1]. The question is how to distinguish a reconstruction from noise from one from legitimate particle images. Figure 1A shows the estimated resolutions of reconstructions from projection images with defined signal-to-noise ratios (SNRimp). Comparison with reconstructions from aligned gaussian noise images provides a lower bound for the SNR that can be tolerated (open circles in Figure 1A). Increasing the number of images suppresses noise, giving a relationship between the product of SNR with the number of images and the resolution obtained (Figure 1B). Therefore, given the number of images contributing to a reconstruction with a defined SNR, and considering alignment errors (see below), a particular resolution should be expected. Any excess in images used in a reconstruction may signal validity issues.