3.5.3 Post-processing to Maximize Signal in Tomograms
Post-processing of the tomogram depends upon the biological question: cell biological questions tend to have the tomogram as the final product for interpretation,
while more structural biological questions will involve an additional, subtomogram
averaging step. In both cases, however, the aim of post-processing is the same:
maximization of relevant signal for accurate interpretation of the dataset to shed
light on the biological question. Interpretation often involves visualization of the
tomogram in 3-D (instead of 2-D slices through the tomographic data) via volume
rendering or, more often, 3-D surface representations using segmentation or isosurfaces. To get to such a 3-D representation a number of noise-reduction
approaches can be taken.
If the final image is a tomogram of a unique specimen, signal at resolutions
lower than a few nanometres is overwhelmed by noise, and filtering is therefore
crucial to optimize more relevant medium- and low-resolution signal for interpretation or segmentation. Filtering is fully treated in Chaps. 7 and 11; as an overview,
filters take various forms: linear, non-linear, and anisotropic, and the choice of
which to use depends on the problem and available resources [81]. Linear filters act
uniformly across the tomogram independent of the local voxel values; non-linear
filters modulate their effect depending upon local voxel values (therefore, for
example, filtering strongly in areas lacking sharp edges, but less strongly in the
presence of edges); while anisotropic filters apply an anisotropic 3D filter that acts
to filter parallel, but not perpendicular, to edges (therefore retaining edge information, but still removing noise). The simplest linear filter is a low-pass filter (or
Gaussian filter) to remove data beyond the first zero of the CTF. The median filter
is a simple nonlinear filter that takes the middle-ranked voxel value of a kernel of
voxels around the current voxel [82]. Nonlinear anisotropic diffusion is a nonlinear
anisotropic technique that takes into account local structure within the tomogram to
locally and anisotropically filter the tomogram, in effect enhancing edges (by not
applying perpendicular to the edge) while removing noise (by filtering in other
directions) [83]. Nonlinear anisotropic diffusion is generally accepted as the most
effective denoising algorithm for individual tomograms [84], although requires
considerable computational power.
How can the resolution of a tomogram be assessed? The resolution of a unique
tomogram can be cited using a number of criteria [80, 85] as described in Chap. 10.
In essence, a part of the tilt series is excluded from reconstruction and subsequently
used to determine consistency at different spatial frequencies to quantify the point at
which signal-to-noise ratio drops below a threshold. It is important to note that these
numbers are relative values for comparison as opposed to technical ‘resolution’, and
tomogram resolution is invariably highly anisotropic due to missing data [86].
Often resolutions of individual tomograms are expressed informally in terms of
discernible features such as ability to resolve leaflets of phospholipid bilayers.
If the object of interest is present in many identical copies in tomograms, the
very low signal at high resolution can be recovered by averaging the identical
3 Electron Cryo-Tomography
79
Post-processing of the tomogram depends upon the biological question: cell biological questions tend to have the tomogram as the final product for interpretation,
while more structural biological questions will involve an additional, subtomogram
averaging step. In both cases, however, the aim of post-processing is the same:
maximization of relevant signal for accurate interpretation of the dataset to shed
light on the biological question. Interpretation often involves visualization of the
tomogram in 3-D (instead of 2-D slices through the tomographic data) via volume
rendering or, more often, 3-D surface representations using segmentation or isosurfaces. To get to such a 3-D representation a number of noise-reduction
approaches can be taken.
If the final image is a tomogram of a unique specimen, signal at resolutions
lower than a few nanometres is overwhelmed by noise, and filtering is therefore
crucial to optimize more relevant medium- and low-resolution signal for interpretation or segmentation. Filtering is fully treated in Chaps. 7 and 11; as an overview,
filters take various forms: linear, non-linear, and anisotropic, and the choice of
which to use depends on the problem and available resources [81]. Linear filters act
uniformly across the tomogram independent of the local voxel values; non-linear
filters modulate their effect depending upon local voxel values (therefore, for
example, filtering strongly in areas lacking sharp edges, but less strongly in the
presence of edges); while anisotropic filters apply an anisotropic 3D filter that acts
to filter parallel, but not perpendicular, to edges (therefore retaining edge information, but still removing noise). The simplest linear filter is a low-pass filter (or
Gaussian filter) to remove data beyond the first zero of the CTF. The median filter
is a simple nonlinear filter that takes the middle-ranked voxel value of a kernel of
voxels around the current voxel [82]. Nonlinear anisotropic diffusion is a nonlinear
anisotropic technique that takes into account local structure within the tomogram to
locally and anisotropically filter the tomogram, in effect enhancing edges (by not
applying perpendicular to the edge) while removing noise (by filtering in other
directions) [83]. Nonlinear anisotropic diffusion is generally accepted as the most
effective denoising algorithm for individual tomograms [84], although requires
considerable computational power.
How can the resolution of a tomogram be assessed? The resolution of a unique
tomogram can be cited using a number of criteria [80, 85] as described in Chap. 10.
In essence, a part of the tilt series is excluded from reconstruction and subsequently
used to determine consistency at different spatial frequencies to quantify the point at
which signal-to-noise ratio drops below a threshold. It is important to note that these
numbers are relative values for comparison as opposed to technical ‘resolution’, and
tomogram resolution is invariably highly anisotropic due to missing data [86].
Often resolutions of individual tomograms are expressed informally in terms of
discernible features such as ability to resolve leaflets of phospholipid bilayers.
If the object of interest is present in many identical copies in tomograms, the
very low signal at high resolution can be recovered by averaging the identical
3 Electron Cryo-Tomography
79