Fourier-based multiple-slice reconstruction in cryo-electron tomography

A tomogram is reconstructed from the micrographs of the tilt series using cryo-electron tomography (cryoET). Reconstruction frequently integrates image processing steps, such as filtering and contrast transfer function (CTF) correction, to support the downstream analysis of cellular and viral structures. Most image processing steps are based on Fourier space analysis, which is theoretically more efficient to be implemented in Fourier space than in real space. However, the substantial dimensions of tomograms present significant challenges for reconstruction and processing in Fourier space. Consequently, real-space reconstruction is prevalent in current practice. In this study, we proposed a Fourier-space algorithm for tomogram reconstruction, named MUltiple Slice Technique (MUST). MUST considers a tomogram composed of multiple parallel slices, with each slice independently reconstructed in Fourier space. A weighting strategy was used to enable MUST to achieve reconstruction compatible with real-space methods, including weighted back-projection (WBP) and the simultaneous iterative reconstruction technique (SIRT). A three-dimensional CTF model was formulated as pairs of conjugate central paraboloids in Fourier space and subsequently implemented for CTF correction in MUST. Alias-free reconstruction and pixel-level parallel computation are key features of MUST, demonstrated through tomogram-based subtomogram averaging at near-atomic resolutions.