The aligned tilt series is next processed to maximize signal, as described fully in
Chap. 11. Optionally binning is performed to further improve signal-to-noise, avoid
unnecessary oversampling, and reduce file size. Typically tilt series are low-pass
filtered to remove data past the first zero of the CTF, or CTF-corrected if the
tomogram will be used for subtomogram averaging. Tilt series may also be
pre-processed by masking the intense signal from gold fiducial markers or contaminants to avoid reconstruction artefacts associated with such very dense materials [66, 77, 78].
Tilt series CTF correction must account for low signal-to-noise ratio (resulting
from the low electron dose per frame) and a defocus gradient (instead of uniform
defocus across the entire image) if the image being processed is not the zero-tilt
image. To boost this low signal-to-noise ratio, power spectra of multiple parts of
multiple images corresponding to the same nominal defocus are usually calculated
[73]. CTF correction may alternatively be deferred until averaging [51].
Tilt images may also be “exposure filtered” as developed for single particle
analysis [79]. This essentially acts as a series of low-pass filters with the frequency
cut-off dependant on the cumulative dose each image has received. Exposure filtering leads to an increase in the SNR, giving higher contrast tomograms, and easier
subtomogram alignment. However, as it results in the dampening of thon rings it
should be performed after CTF correction.
3.5.2 Reconstruction
Tomographic reconstruction involves calculating a single 3-D reconstruction from
the multiple aligned 2-D projection images in the tilt series and is covered in-depth
in Chap. 8. Reconstruction can be performed using a variety of algorithms although
in practice the weighted back-projection (WBP) algorithm is most often used [66],
or a family of iterative algorithms typified by the SIRT algorithm [72]. WBP
involves “back projecting” the densities from each tilt series image back through a
volume; these projections reinforce in areas of the volume corresponding to the
specimen structure, with down-weighting of the disproportionately high contribution of the low spatial frequencies. WBP is fast but produces low signal-to-noise
ratio reconstructions. Recent increases in computational power has enabled routine
use of the SIRT algorithm; SIRT iteratively minimizes discrepancies between the
input tilt series and calculated projected tilt series from the tomogram to produce
higher contrast reconstructions, although may attenuate signal at high spatial frequencies. If the dataset collected was dual-axis, the conventional approach is to
calculate and merge two single-axis tomograms; in the absence of significant
specimen warping however, it is possible to attain higher quality reconstructions by
aligning both axes simultaneously using a fiducial-less approach [67, 80].
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Chap. 11. Optionally binning is performed to further improve signal-to-noise, avoid
unnecessary oversampling, and reduce file size. Typically tilt series are low-pass
filtered to remove data past the first zero of the CTF, or CTF-corrected if the
tomogram will be used for subtomogram averaging. Tilt series may also be
pre-processed by masking the intense signal from gold fiducial markers or contaminants to avoid reconstruction artefacts associated with such very dense materials [66, 77, 78].
Tilt series CTF correction must account for low signal-to-noise ratio (resulting
from the low electron dose per frame) and a defocus gradient (instead of uniform
defocus across the entire image) if the image being processed is not the zero-tilt
image. To boost this low signal-to-noise ratio, power spectra of multiple parts of
multiple images corresponding to the same nominal defocus are usually calculated
[73]. CTF correction may alternatively be deferred until averaging [51].
Tilt images may also be “exposure filtered” as developed for single particle
analysis [79]. This essentially acts as a series of low-pass filters with the frequency
cut-off dependant on the cumulative dose each image has received. Exposure filtering leads to an increase in the SNR, giving higher contrast tomograms, and easier
subtomogram alignment. However, as it results in the dampening of thon rings it
should be performed after CTF correction.
3.5.2 Reconstruction
Tomographic reconstruction involves calculating a single 3-D reconstruction from
the multiple aligned 2-D projection images in the tilt series and is covered in-depth
in Chap. 8. Reconstruction can be performed using a variety of algorithms although
in practice the weighted back-projection (WBP) algorithm is most often used [66],
or a family of iterative algorithms typified by the SIRT algorithm [72]. WBP
involves “back projecting” the densities from each tilt series image back through a
volume; these projections reinforce in areas of the volume corresponding to the
specimen structure, with down-weighting of the disproportionately high contribution of the low spatial frequencies. WBP is fast but produces low signal-to-noise
ratio reconstructions. Recent increases in computational power has enabled routine
use of the SIRT algorithm; SIRT iteratively minimizes discrepancies between the
input tilt series and calculated projected tilt series from the tomogram to produce
higher contrast reconstructions, although may attenuate signal at high spatial frequencies. If the dataset collected was dual-axis, the conventional approach is to
calculate and merge two single-axis tomograms; in the absence of significant
specimen warping however, it is possible to attain higher quality reconstructions by
aligning both axes simultaneously using a fiducial-less approach [67, 80].
78
J. L. Ferreira et al.