holder in the microscope (a tilt series). Electron cryotomography is the unique
approach to determine the architecture of pleomorphic biological specimens.
Radiation damage imposes a limit on the number of low-dose images that may be
recorded in a tilt-series of a frozen-hydrated specimen. The acquired tilt-series thus
possesses a low SNR. In addition, there is usually a restriction on the range of views
that may be obtained of the specimen, resulting in a ‘‘missing wedge’’ of data.
In electron tomography, the final volume (tomogram) is obtained through
reconstruction from angular tilt projections of the specimen, typically from À70
to
þ 70
, with 2
to 4
increments. The tomographic reconstruction has been referred
to as a “severely ill-posed” inverse problem because of the limited range of angular
projections and the limited sampling rate in the image acquisition protocol [10, 11,
37]. Computational procedures that reduce this ill-posedness are termed “regularization”. The ill-posedness can be reduced by collecting additional information
from the sample. In electron tomography this can be achieved by modifying the
acquisition geometry, for example, by collecting a dual tilt series [19] or by
obtaining better images, such as with direct detector devices that have recently
become available. Even so, the missing data still produces artefacts, and computational regularization may be necessary.
A common application of cryotomography is the imaging of thick specimens
that present additional problems of multiple scattering causing further degradation
of the signal available in the images. Specimen thickness increases with increasing
tilt angle. Electrons that are inelastically scattered contribute only noise to the image
that may be removed by energy filtration, and in the future thicker specimens may
also benefit from chromatic aberration correction [16].
Another type of problem results from the use of gold nanoparticles as fiducial
markers in specimens for alignment or as immunolabels to identify molecules in the
images and tomograms. Such particles are electron dense and are located proximal
to regions of low density [7, 30]. These grayscale irregularities in tilt projections
result in edge-gradient effects that obscure surrounding features in reconstructed
volumes [6, 29]. Those artefacts are streak-shaped in filtered back projection
(FBP) reconstruction [6, 9] and can be reduced by pre-reconstruction signal optimization approaches [28].
In practice, the low SNR of reconstructed data combined with missing data
makes the identification and analysis of biological features in 3D tomograms
challenging [32]. Signal optimization is essential for visualization as well computational segmentation of features in low contrast, noisy tomograms.
This chapter describes signal optimization procedures for cryotomograms. Many
have analogues as filters for 2D image analysis and may be linear or non-linear, and
the effect on voxel densities may be isotropic or anisotropic. Sections 11.2 and 11.3
discuss signal optimization in Fourier and real space respectively.
Several approaches have been described for using post-reconstruction
diffusion-based methods to aid the interpretability of electron tomograms through
local regularization [21, 32]. Within the last decade, Non-linear Anisotropic
Diffusion (NAD) became the state of the art method for denoising reconstructed
data [12, 13, 15, 38, 40]. Many of the procedures described for post-reconstruction
284
M. Maiorca and P. B. Rosenthal
approach to determine the architecture of pleomorphic biological specimens.
Radiation damage imposes a limit on the number of low-dose images that may be
recorded in a tilt-series of a frozen-hydrated specimen. The acquired tilt-series thus
possesses a low SNR. In addition, there is usually a restriction on the range of views
that may be obtained of the specimen, resulting in a ‘‘missing wedge’’ of data.
In electron tomography, the final volume (tomogram) is obtained through
reconstruction from angular tilt projections of the specimen, typically from À70
to
þ 70
, with 2
to 4
increments. The tomographic reconstruction has been referred
to as a “severely ill-posed” inverse problem because of the limited range of angular
projections and the limited sampling rate in the image acquisition protocol [10, 11,
37]. Computational procedures that reduce this ill-posedness are termed “regularization”. The ill-posedness can be reduced by collecting additional information
from the sample. In electron tomography this can be achieved by modifying the
acquisition geometry, for example, by collecting a dual tilt series [19] or by
obtaining better images, such as with direct detector devices that have recently
become available. Even so, the missing data still produces artefacts, and computational regularization may be necessary.
A common application of cryotomography is the imaging of thick specimens
that present additional problems of multiple scattering causing further degradation
of the signal available in the images. Specimen thickness increases with increasing
tilt angle. Electrons that are inelastically scattered contribute only noise to the image
that may be removed by energy filtration, and in the future thicker specimens may
also benefit from chromatic aberration correction [16].
Another type of problem results from the use of gold nanoparticles as fiducial
markers in specimens for alignment or as immunolabels to identify molecules in the
images and tomograms. Such particles are electron dense and are located proximal
to regions of low density [7, 30]. These grayscale irregularities in tilt projections
result in edge-gradient effects that obscure surrounding features in reconstructed
volumes [6, 29]. Those artefacts are streak-shaped in filtered back projection
(FBP) reconstruction [6, 9] and can be reduced by pre-reconstruction signal optimization approaches [28].
In practice, the low SNR of reconstructed data combined with missing data
makes the identification and analysis of biological features in 3D tomograms
challenging [32]. Signal optimization is essential for visualization as well computational segmentation of features in low contrast, noisy tomograms.
This chapter describes signal optimization procedures for cryotomograms. Many
have analogues as filters for 2D image analysis and may be linear or non-linear, and
the effect on voxel densities may be isotropic or anisotropic. Sections 11.2 and 11.3
discuss signal optimization in Fourier and real space respectively.
Several approaches have been described for using post-reconstruction
diffusion-based methods to aid the interpretability of electron tomograms through
local regularization [21, 32]. Within the last decade, Non-linear Anisotropic
Diffusion (NAD) became the state of the art method for denoising reconstructed
data [12, 13, 15, 38, 40]. Many of the procedures described for post-reconstruction
284
M. Maiorca and P. B. Rosenthal