pre-processing the images, as well as post-processing to facilitate interpretation. In
real space, we typically normalize the original tilt series, remove high contrast
features such as X-ray specks and fiducial markers, and do limited denoising (see
Sect. 8.4). When we desire to recover high resolution information, we need to
correct for the contrast transfer function (CTF) in frequency space (the equivalent of
the point spread function in real space—see Sect. 8.5).
Post-processing is largely concerned with removing noise (see Sect. 8.6) and
compensating for missing information. The low dose used in tomography (to avoid
radiation damage) means a low SNR and noisy tomograms. The various reconstruction algorithms show differences in the noise level of the initially reconstructed
tomogram, but there is almost always a need for further denoising. An integral second
step in reconstruction is therefore to remove sufficient noise to allow proper interpretation (segmentation is very sensitive to noise—see Chap. 12). All denoising
algorithms decrease detail in the tomograms (see Chap. 11). Therefore, the user
determines the level of denoising with the aim of emphasizing the desired detailed
structures with as little confusion attributed to noise as possible (see Sect. 8.6).
The limited tilt range in the electron microscope as well as a finite number of
images give rise to missing information (i.e., poorly represented regions in frequency space—see Sect. 8.7). The result is highly anisotropic resolution, with
apparent elongation of features in the beam direction and suppression of features
perpendicular to the tilt axis. Dual and conical tilt acquisition schemes alleviate
some of the loss, but to a limited extent. If we image a specimen with a repeating
structure (such as isolated viruses), we can average such structures to decrease
noise, fill in missing information and recover higher resolution information (see
Sect. 8.8 and Chap. 9).
Numerous programs have been written to do 3D reconstructions (Table 8.1).
While the basic concepts remain the same, the differences lie in the details of
weighting and interpolation. Many denoising algorithms have been developed to
deal with the typical low SNR in tomograms (Table 8.2). A more comprehensive
list of software packages is available at https://en.wikibooks.org/wiki/Software_
Tools_For_Molecular_Microscopy.
8.2 Integrative Reconstruction
The simplest reconstruction approach is to reverse the projection operation, either in
real space or frequency space. The advantage of a straightforward integration
algorithm is that it involves only the interpolation and weighting issues. Dealing
with noise and missing information is done in subsequent steps.
8 Tomographic Reconstruction from Electron Micrographs
211
real space, we typically normalize the original tilt series, remove high contrast
features such as X-ray specks and fiducial markers, and do limited denoising (see
Sect. 8.4). When we desire to recover high resolution information, we need to
correct for the contrast transfer function (CTF) in frequency space (the equivalent of
the point spread function in real space—see Sect. 8.5).
Post-processing is largely concerned with removing noise (see Sect. 8.6) and
compensating for missing information. The low dose used in tomography (to avoid
radiation damage) means a low SNR and noisy tomograms. The various reconstruction algorithms show differences in the noise level of the initially reconstructed
tomogram, but there is almost always a need for further denoising. An integral second
step in reconstruction is therefore to remove sufficient noise to allow proper interpretation (segmentation is very sensitive to noise—see Chap. 12). All denoising
algorithms decrease detail in the tomograms (see Chap. 11). Therefore, the user
determines the level of denoising with the aim of emphasizing the desired detailed
structures with as little confusion attributed to noise as possible (see Sect. 8.6).
The limited tilt range in the electron microscope as well as a finite number of
images give rise to missing information (i.e., poorly represented regions in frequency space—see Sect. 8.7). The result is highly anisotropic resolution, with
apparent elongation of features in the beam direction and suppression of features
perpendicular to the tilt axis. Dual and conical tilt acquisition schemes alleviate
some of the loss, but to a limited extent. If we image a specimen with a repeating
structure (such as isolated viruses), we can average such structures to decrease
noise, fill in missing information and recover higher resolution information (see
Sect. 8.8 and Chap. 9).
Numerous programs have been written to do 3D reconstructions (Table 8.1).
While the basic concepts remain the same, the differences lie in the details of
weighting and interpolation. Many denoising algorithms have been developed to
deal with the typical low SNR in tomograms (Table 8.2). A more comprehensive
list of software packages is available at https://en.wikibooks.org/wiki/Software_
Tools_For_Molecular_Microscopy.
8.2 Integrative Reconstruction
The simplest reconstruction approach is to reverse the projection operation, either in
real space or frequency space. The advantage of a straightforward integration
algorithm is that it involves only the interpolation and weighting issues. Dealing
with noise and missing information is done in subsequent steps.
8 Tomographic Reconstruction from Electron Micrographs
211