Single-particle reconstruction of vitrified samples (cryo-electron microscopy, or cryo-EM) provides structural information for a large variety of biological molecules, ranging from small proteins to large macromolecular assemblies in their native state, without the need to produce crystals. However, for ab initio modeling, it is a great challenge to produce density maps, because of the extremely low signal to noise ratio (SNR) of the projection images. A crucial step is alignment and averaging of the 2D projection images, which are from similar viewing directions, a procedure known as “class averaging”. Images from the same projection angles should be identified, aligned and averaged to achieve a higher signal-to-noise ratio.

We introduce a new class averaging method that achieves robust viewing angle classification without prior knowledge of the molecule. The algorithm has three steps: Fourier-Bessel steerable PCA for image compression and de-noising, bispectrum-like rotational invariant feature extraction for classification, and Vector Diffusion Maps application for more robust nearest neighbor search and rotational alignment. Our 3D ab initial reconstruction of 50S ribosomal subunit density map achieves 11.4 Angstrom resolution.