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8.6.5.1 Transmission Electron Microscopy

Transmission electron microscopy is the process of using transmission images of electron beams to reveal biological structures on very small dimensions. Typically transmission electron microscopy (TEM) datasets are produced using a dye that highlights regions of interest, e.g. the interior of a microscopic structure, such as a cell (see Fig. 8.22(a)). There are technical limits to the projection angles from which data can be measured. These limits are due to the mechanical apparatus used to tilt the specimens and the trade-off between the destructive effects of electron energy and the effective specimen thickness, which increases with tilt angle. Usually, the maximum tilt angle is restricted to about ±60-70°. Figure 8.22(b) shows an illustration of the geometry of this limited-angle scenario. The TEM reconstruction problem is further aggravated by the degree of electron scattering, which results in projection images (sinograms) that are noisy relative to many other modalities, e.g. X-ray CT. Finally, due to the flexible nature of biological objects and the imperfections in the tilting mechanism, the objects undergo some movements while being tilted. Manual alignment procedures used to account for this tend to produce small misregistration errors.

We applied the proposed algorithm to 3D TEM data obtained from a 3 MeV electron microscope. This 3D dataset consists of 67 tilt series images, each corresponding to one view of the projection. Each tilt series image is of size 424 x 334. The volume reconstructed by FBP is of size 424 x 424 x 334. Figures 8.23(a)

Figure8.23: 2D slice of dendrite data: (a) sinogram of one slice, (b) sinogram estimated by the proposed method, (c) back projection showing artifacts, (d) initial model obtained by thresholding the back projection (white curve overlaid on the back projection), and (e) final surface estimate.

Figure8.23: 2D slice of dendrite data: (a) sinogram of one slice, (b) sinogram estimated by the proposed method, (c) back projection showing artifacts, (d) initial model obtained by thresholding the back projection (white curve overlaid on the back projection), and (e) final surface estimate.

and (b) show the sinogram corresponding to a single slice of this dataset and the estimate of the same sinogram created by the method. Figure 8.23(e) shows the surface estimate intersecting this slice overlaid on the back projected slice. Some structures not seen in the back projection are introduced in the final estimation, but the orientation of the structures introduced suggests that these are valid features that were lost due to reconstruction artifacts from the FBP. Also, the proposed method captures line-by-line brightness variations in the input sinogram (as explained in Section 8.6.2.1). This suggests that the density estimation procedure is correct.

Figure 8.24 shows the 3D initialization and the final 3D surface estimate. The figure also shows enlarged initial and final versions of a small section of the surface. Computing the surface estimate for the TEM dendrite with 150 iterations took approximately 3 hours on a single 300 MHz processor of a Silicon Graphics Onyx2 workstation. We consider these results positive for several reasons. First, the biology is such that one expects the spines (small protrusions) to be connected to the dendrite body. The proposed method clearly establishes those connections, based solely on consistency of the model with the projected data. The second piece of evidence is the shapes of the spines themselves. The reconstructed model shows the recurrence of a characteristic shape—a long thin spine with a cup-like structure on the end. This characteristic structure, which

Figure 8.24: 3D results: (a) surface initialization, (b) final surface estimated after 150 iterations, (c) a portion of the initial surface enlarged, and (d) the corresponding portion in the final surface.

Figure 8.24: 3D results: (a) surface initialization, (b) final surface estimated after 150 iterations, (c) a portion of the initial surface enlarged, and (d) the corresponding portion in the final surface.

often fails to show up in the FBP reconstruction, does appear quite regularly in hand-segmentations of the same datasets.

8.6.5.2 Sinogram Extrapolation

The fitting of surfaces to this data is a simplification. It is justified in the context of segmentation, but there are underlying inhomogeneities in the density of this specimen, which could be indicative of relevant structures. Thus for some applications direct visualization of the measured data, by volume rendering, offers advantages over the segmented surfaces. We propose to use the surface estimation algorithm as a mechanism for estimating the missing data in the sinograms.

Figures 8.25(a) and (b) show the input sinogram and the sinogram of the estimated model (for one slice) of the TEM dendrite data. The estimated sinogram demonstrates that the surface estimation method recovers the missing information in a reasonable way. Thus, we combine the sinograms from the model with original sinograms to produce a "full" sinogram that still contains all of the

Figure 8.25: Sinogram extrapolation for slice number 150 of dendrite data: (a) input sinogram, (b) sinogram estimated by the proposed method, (c) augmented sinogram constructed using original data and estimating missing data from the segmentation, and (d) FBP reconstruction of the augmented sinogram.

Figure 8.25: Sinogram extrapolation for slice number 150 of dendrite data: (a) input sinogram, (b) sinogram estimated by the proposed method, (c) augmented sinogram constructed using original data and estimating missing data from the segmentation, and (d) FBP reconstruction of the augmented sinogram.

orginal, measured data. FBP reconstructions from such augmented sinograms should have fewer limited-angle streak artifacts.

We demonstrate this by comparing volume renderings with and without the augmentation. We create augmented sinograms by using sinogram data from the estimated model only where the data is missing from the measured sinograms. The augmented sinogram for a single slice is shown in Fig. 8.25(c). The slice reconstructed (FBP) from the augmented sinogram is shown in Fig. 8.25(d). Note that this reconstructed slice does not contain the limited-angle artifacts that appear in the slice in Fig. 8.23(c). Maximum intensity projection (MIP) volume renderings of the volume created from original sinograms and the volume created from augmented sinograms are compared in Fig. 8.26. The main body of the dendrite, which exhibited a very convoluted and fuzzy boundary, shows better definition. Also, several of the spines which were dangling in the original reconstruction are now connected.

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