Subtomogram alignment by adaptive Fourier coefficient thresholding

In the past few years, three-dimensional (3D) subtomogram alignment has become an important tool in cryo-electron tomography (CET). This technique allows one to produce higher resolution images of structures which can not be reconstructed using single-particle methods. Building on previous work, we present a new dissimilarity measure between subtomograms that works well for the noisy images that often occur in CET images. A technique that is more robust to noise provides the ability to analyze macromolecules in thicker samples such as whole cells or lower the defocus in thinner samples to push the first zero of the Contrast Transfer Function (CTF). Our method, Threshold Constrained Cross-Correlation (TCCC), uses statistics of the noise to automatically select only a small percentage of the Fourier coefficients to compute the cross-correlation, which has two main advantages: first, it reduces the influence of the noise by looking at only those peaks dominated by signal; and second, it avoids the missing wedge normalization problem since we consider the same number of coefficients for all possible pairs of subtomograms. We present results with synthetic and real data to compare our approach with other existing methods under different SNR and missing wedge conditions, and show that TCCC improves alignment results for datasets with SNR < 0.1. We have made our source code freely available for the community.