Abstract
The limited specimen tilting range that is typically available in electron tomography gives rise to a region in the Fourier space of the reconstructed object where experimental data are unavailable – the missing wedge. Since this region is sharply delimited from the area of available data, the reconstructed signal is typically hampered by convolution with its impulse response, which gives rise to the well-known missing wedge artefacts in 3D reconstructions. Despite the recent progress in the field of reconstruction and regularization techniques, the missing wedge artefacts remain untreated in most current reconstruction workflows in structural biology. Therefore we have designed a simple Fourier angular filter that effectively suppresses the ray artefacts in the single-axis tilting projection acquisition scheme, making single-axis tomographic reconstructions easier to interpret in particular at low signal-to-noise ratio in acquired projections. The proposed filter can be easily incorporated into current electron tomographic reconstruction schemes.
Highlights
Three-dimensional electron tomographic reconstructions are produced by the acquisition of a set of tilted projections that are subsequently aligned and subjected to a reconstruction algorithm
The computed reconstructions typically suffer from a number of artefacts arising from an imprecise projection alignment, from the structural instability of specimens during tomogram acquisition, and from the presence of the missing wedge region in the Fourier space of reconstructions, which remains free of experimental data due to the limited possibility of specimen tilting in transmission electron microscopes (TEMs)
Since the geometry of the missing wedge in the Fourier space of the reconstructed object is independent of the Y position at the single-axis tilting acquisition scheme, angular filtering can be parallelized to speed up its application
Summary
Three-dimensional electron tomographic reconstructions are produced by the acquisition of a set of tilted projections that are subsequently aligned and subjected to a reconstruction algorithm. The computed reconstructions typically suffer from a number of artefacts arising from an imprecise projection alignment, from the structural instability of specimens during tomogram acquisition, and from the presence of the missing wedge region in the Fourier space of reconstructions, which remains free of experimental data due to the limited possibility of specimen tilting in transmission electron microscopes (TEMs). The proposed angular filter can be applied either consecutively to all X–Z planes of Fourier transformed reconstructions by simple multiplication or to aligned stacks of projections prior to 3D reconstruction. Since the geometry of the missing wedge in the Fourier space of the reconstructed object is independent of the Y position at the single-axis tilting acquisition scheme, angular filtering can be parallelized to speed up its application. 1 bfly20-4-0.5-15-4-10 5.01 2.93 2.85 2.71 À0.04 À2.38 3.29 2.82 0.52 À2.59 À6.18 À6.35 2 bfly20-4-0.2-15-4-10 7.85 7.84 7.64 7.34 1.05 À4.38 7.89 7.63 3.09 À2.90 À9.80 À10.25 3 bfly20-4-0.13-15-4-10 11.08 11.04 10.79 10.36 1.95 À5.27 11.10 10.79 5.01 À2.56 À11.31 À11.81 4 bfly20-4-0.2-25-4-20 7.42 7.41 7.26 7.10 2.77 À0.83 7.45 7.32 4.81 1.62 À2.04 À2.22 5 bfly20-4-0.2-8-2-4 8.16 8.13 7.74 6.80 À8.33 À21.50 8.19 7.45 À6.84 À25.36 À47.77 À47.99 6 bfly10-4-0.2-15-4-10 4.48 4.48 4.36 4.17 0.08 À3.45 4.51 4.35 1.22 À2.96 À7.72 À8.04 7 bfly40-4-0.2-15-4-10 15.54 15.43 15.12 14.53 3.68 À5.64 15.54 15.16 7.98 À1.47 À12.32 À12.87
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