Orientation Estimation | ASPIRE - Princeton University

$Fourier Slice Theorem$ The Fourier Projection Slice Theorem implies that the orientations of three projection images can be determined from their common lines, which is the foundation of the angular reconstitution method (van Heel 1987; Vainshtein and Goncharov 1986). The orientations of the remaining particles can be deduced in a sequential manner from their common lines with the previously orientation-assigned particles. However, conventional SPR algorithms fail with particles that are too small, with images that are too noisy, or at resolutions where the signal-to-noise ratio (SNR) becomes too small. $Angular Reconstitution$

Our toolbox provide several common-line based algorithms that utilize the information in the common lines between all pairs of images simultaneously, leading to an assignment of orientations that is as consistent as possible with the common lines. Our approaches use convex optimization and semidefinite relaxation, spectral methods and Bayesian approaches, and work for both uniform and non-uniform viewing angle distributions. It is recommended to use our orientation assignment algorithms on class averages rather than on the raw images whose SNR is typically too low. Our algorithms assume a non-symmetric molecule; In the future we plan to extend the algorithm to deal with molecules with non-trivial point-group symmetry.