Fast Alignment of Limited Angle Tomograms by projected Cross Correlation

Volume alignment is a computationally intensive task. In Subtomogram Averaging (StA) from electron cryotomograms (CryoET), thousands of subtomograms are aligned to a reference, which may take hours until days of computational time. CryoET datasets contain a limited number of noisy projections, with very low signal–to–until ratio (SNR). The noisy subtomograms are aligned to a reference using cross—correlation, an operation that can be optimized when working with limited angle tomograms (LAT), as they are sparse in Fourier space. We propose a projected cross–correlation (pCC) algorithm, a faster approach to computing the cross—correlation between a limited angle (sub)–tomogram and a given reference, and we use pCC to design a new procedure for volume alignment. pCC employs the projections to calculate the cross–correlation with lower computational complexity, as it works with a set 2D projections instead of volumes. With this, we propose the Substacks Averaging (SsA) method as an alternative to the conventional Subtomogram Averaging (StA). Our results on test data shows that SsA is considerably faster than the reference StA implementation: for 41 projections (k= 41) and N=200, the SsA is 35 times faster, and for N=320, is 150 times faster. Furthermore, SsA results in higher precision of alignment of subtomograms at different noise levels.