reconstruction techniques can inherently produce maps with less noise (e.g., the
IMOD SIRT implementation used in Fig. 8.2c). In particular, the integrative reconstruction algorithms incorporate sufficient noise to require subsequent denoising
(Fig. 8.2a, b). Appropriate denoising can allow the analysis of the locations and copy
numbers of individual proteins [51].
Tomograms from cryo-EM micrographs are typically very noisy due to the low
dose used in data acquisition. The goal of denoising is to make desirable objects
and features stand out from the background (e.g., when an isosurface is calculated).
Denoising can even be done on the original tilt series, preceding 3D reconstruction
[37, 41] (see Sect. 8.5). Any form of denoising is a smoothing operation limited to
spatially defined kernels. Many algorithms are iterative, requiring the user to choose
a stopping point. The typical parameters include the size of the kernel, some kernel
weighting function and the number of iterations. In each case we have to judge
when a denoising operation has removed enough noise (and artifacts) without
degrading the details of interest. The algorithm and parameters chosen therefore
reflects this subjectivity.
8.6.1 Low-Pass Filter
The simplest filters remove high frequency noise. Two commonly used real-space
filters are local averaging (moving window) and Gaussian smoothing. Both these
constitute convolution with a local kernel where the size of the kernel and Gaussian
width are user-selected parameters. In frequency space, a high-frequency limit with
a hard or soft cutoff can be imposed. The frequency limit and the soft cutoff width
are likewise user-selected.
8.6.2 Iterative Median Filter
For a median filter, the middle-ranked value within a kernel is taken as the new
value of a pixel. This is a particularly simple method to eliminate extreme pixel
values (Fig. 8.4a). The user typically decides the size of the kernel and the number
of iterations, both smoothing the map with larger values (2–3 iterations are typically
sufficient). Excessive iterations may result in the loss of information as homogenous
median blocks are expanding [52].
8.6.3 Bilateral Filter
The bilateral filter calculates a value for a pixel integrating over a kernel with both
distance and density difference functions (Fig. 8.4b) [53, 54].
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J. Bernard Heymann
IMOD SIRT implementation used in Fig. 8.2c). In particular, the integrative reconstruction algorithms incorporate sufficient noise to require subsequent denoising
(Fig. 8.2a, b). Appropriate denoising can allow the analysis of the locations and copy
numbers of individual proteins [51].
Tomograms from cryo-EM micrographs are typically very noisy due to the low
dose used in data acquisition. The goal of denoising is to make desirable objects
and features stand out from the background (e.g., when an isosurface is calculated).
Denoising can even be done on the original tilt series, preceding 3D reconstruction
[37, 41] (see Sect. 8.5). Any form of denoising is a smoothing operation limited to
spatially defined kernels. Many algorithms are iterative, requiring the user to choose
a stopping point. The typical parameters include the size of the kernel, some kernel
weighting function and the number of iterations. In each case we have to judge
when a denoising operation has removed enough noise (and artifacts) without
degrading the details of interest. The algorithm and parameters chosen therefore
reflects this subjectivity.
8.6.1 Low-Pass Filter
The simplest filters remove high frequency noise. Two commonly used real-space
filters are local averaging (moving window) and Gaussian smoothing. Both these
constitute convolution with a local kernel where the size of the kernel and Gaussian
width are user-selected parameters. In frequency space, a high-frequency limit with
a hard or soft cutoff can be imposed. The frequency limit and the soft cutoff width
are likewise user-selected.
8.6.2 Iterative Median Filter
For a median filter, the middle-ranked value within a kernel is taken as the new
value of a pixel. This is a particularly simple method to eliminate extreme pixel
values (Fig. 8.4a). The user typically decides the size of the kernel and the number
of iterations, both smoothing the map with larger values (2–3 iterations are typically
sufficient). Excessive iterations may result in the loss of information as homogenous
median blocks are expanding [52].
8.6.3 Bilateral Filter
The bilateral filter calculates a value for a pixel integrating over a kernel with both
distance and density difference functions (Fig. 8.4b) [53, 54].
224
J. Bernard Heymann