missing regions in frequency space can suppress these artifacts to some extent [64,
65]. The difference observed between WBP and FSR in terms of these artifacts [12]
is likely due to more appropriate weighting in these transition regions in the latter.
8.7.2 Recovering Missing Information
Information that is not recorded cannot be recovered. However, if we impose
constraints on what the data should be, the relationships inherent in these constraints can be used to fill in some of the missing information. Carazo and
Carrascoza [66] introduced the constraints-based method of projection onto convex
sets (POCS) into the cryo-EM field. However, the results were disappointing and
little progress has been made [11]. Deng et al. [67] developed a compressed sensing
approach to fill in some of the missing information with promising results. Here the
principle used is that most of the specimen is solvent, meaning that the matrix
relating the reconstruction volume to the micrographs is largely sparse. The
introduction of external information such as constraints is partially subjective and
should be considered with care.
8.7.3 Visual Assessment
The most common assessment of the quality of tomograms involves examining
slices in the xy plane as shown in Figs. 8.2 and 8.4 (i.e., perpendicular to the
electron beam for the 0° micrograph). Isosurface renderings of denoised tomograms
reveal the anisotropy of details (Fig. 8.5). The densities are typically elongated in
the z direction due to the missing wedge. Tubular structures in the xy plane perpendicular to the tilt axis are usually poorly represented.
The different reconstruction algorithms also result in tomograms with variable
interpretability. Figure 8.5 shows three reconstructions of a clathrin basket oriented to
show a hexagon in the front face. It is hard to make out the hexagon in the WBP map
(Fig. 8.5a), while the FSR map (Fig. 8.5b) is easier to interpret with five of the
hexagon sides visible. The SIRT map (Fig. 8.5c) seems to be relatively noise free, but
only four sides of the hexagon is apparent.
8.7.4 Resolution Estimation
While the quality of a tomographic reconstruction is often judged by eye, it is
important to have a more objective measure of resolution (see Chap. 10). However,
any measure reflects the anisotropy derived from the geometry of data acquisition.
For a single tilt experiment, the resolution is the highest along the tilt axis as shown
8 Tomographic Reconstruction from Electron Micrographs
227
65]. The difference observed between WBP and FSR in terms of these artifacts [12]
is likely due to more appropriate weighting in these transition regions in the latter.
8.7.2 Recovering Missing Information
Information that is not recorded cannot be recovered. However, if we impose
constraints on what the data should be, the relationships inherent in these constraints can be used to fill in some of the missing information. Carazo and
Carrascoza [66] introduced the constraints-based method of projection onto convex
sets (POCS) into the cryo-EM field. However, the results were disappointing and
little progress has been made [11]. Deng et al. [67] developed a compressed sensing
approach to fill in some of the missing information with promising results. Here the
principle used is that most of the specimen is solvent, meaning that the matrix
relating the reconstruction volume to the micrographs is largely sparse. The
introduction of external information such as constraints is partially subjective and
should be considered with care.
8.7.3 Visual Assessment
The most common assessment of the quality of tomograms involves examining
slices in the xy plane as shown in Figs. 8.2 and 8.4 (i.e., perpendicular to the
electron beam for the 0° micrograph). Isosurface renderings of denoised tomograms
reveal the anisotropy of details (Fig. 8.5). The densities are typically elongated in
the z direction due to the missing wedge. Tubular structures in the xy plane perpendicular to the tilt axis are usually poorly represented.
The different reconstruction algorithms also result in tomograms with variable
interpretability. Figure 8.5 shows three reconstructions of a clathrin basket oriented to
show a hexagon in the front face. It is hard to make out the hexagon in the WBP map
(Fig. 8.5a), while the FSR map (Fig. 8.5b) is easier to interpret with five of the
hexagon sides visible. The SIRT map (Fig. 8.5c) seems to be relatively noise free, but
only four sides of the hexagon is apparent.
8.7.4 Resolution Estimation
While the quality of a tomographic reconstruction is often judged by eye, it is
important to have a more objective measure of resolution (see Chap. 10). However,
any measure reflects the anisotropy derived from the geometry of data acquisition.
For a single tilt experiment, the resolution is the highest along the tilt axis as shown
8 Tomographic Reconstruction from Electron Micrographs
227