# Deep image prior for limited-angle electron tomography

Zineb Saghi, Laure Guetaz, Thomas David, Philippe Ciuciu

► To cite this version:

Zineb Saghi, Laure Guetaz, Thomas David, Philippe Ciuciu. Deep image prior for limited-angle electron tomography. BIO Web of Conferences, 2024, 129, pp.02012. 10.1051/bioconf/202412902012. hal-04747438

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Deep image prior for limited-angle electron tomography

Dr Zineb SAGHI¹, Laure Guetaz², Thomas David², Philippe Ciuciu³, Zineb Saghi¹

¹Univ. Grenoble Alpes, CEA, Leti, F-38000, Grenoble, France, ²Univ. Grenoble Alpes, CEA, Liten, F-38000, Grenoble, France, ³Univ. Paris Saclay, CEA-NeuroSpin, INRIA, Parietal, Gif-sur-Yvette, France

## Background incl. aims

Electron Tomography (ET) is a widely used technique for the 3D characterization of nanomaterials. To obtain faithful reconstructions, high-quality projection data must be acquired over the full 180° tilt range and at tilt increments of 1-2°. However, for slab-like sample geometries, the tilt range is often limited due to geometric restrictions within the TEM, and a large tilt increment is used to minimize the total electron dose. These restrictions lead to blurring and distortions in reconstructions obtained with conventional algorithms such as simultaneous iterative reconstruction technique (SIRT). Compressed sensing (CS) approaches have been introduced to improve the quality of reconstructions. Although CS techniques outperform conventional methods in sparse-view acquisition scenarios, they fail to correct artifacts due to the limited angular range. Data-driven deep learning (DL) approaches have been proposed for denoising and distortion correction of X-ray tomography and ET reconstructions. Although promising, these approaches are highly dependent on the availability of high-quality data sets for neural network training. Such data sets are often not available in practice, making it difficult to apply DL methods to a wide range of samples. Recently, Deep Image Prior (DIP) has been proposed for several image restoration problems, and adapted to limited-angle X-ray tomography. The method uses a neural network as a prior for the reconstruction, but has the advantage of not requiring any training data set, making it suitable for ET applications.

## Methods

In this work, we apply DIP with total variation regularization (DIP-TV) to a sample consisting of carbon-supported platinum nanoparticles (NPs) dispersed on a carbon grid. ADF-STEM and HAADF-STEM tilt series were acquired from -60° to +60° with an increment of 2°, using an FEI Titan Themis operating at 200kV. In HAADF-STEM projections, only Pt NPs were visible, while in ADF-STEM mode, both Pt NPs and C support were visible but the images were affected by diffraction contrast. DIP-TV was applied for 3D reconstruction in both imaging modes, using increments of 2°, 10° and 20°. Results were compared with those obtained with SIRT and CS with TV regularization (CS-TV).

## Results

Figure 1 shows the reconstruction of a slice from ADF-STEM and HAADF-STEM tilt series, obtained with SIRT, CS-TV and DIP-TV. The tilt range is [-60°:+60°]
for all reconstructions, with the missing wedge in the horizontal direction,
while the tilt increment is set to 2°, 10° and 20°. In HAADF-STEM
reconstructions (left), only Pt NPs are visible. SIRT suffers from elongation
artifacts and 'star artifacts' as the tilt increment increases. CS-TV slightly
improves the quality of the reconstructions but suffers from oil painting
effects. DIP-TV reconstructions appear consistent under all acquisition
conditions, with near-spherical, well-contrasted particles. The ADF projections
are more complex, as the carbon support is visible and superposed on the Pt
NPs. SIRT reconstructions suffer from significant artifacts in the support,
which increase as the number of projections is reduced. CS-TV still manages
to reconstruct the particles, but the carbon is not well retrieved. In particular,
for both SIRT and CS-TV reconstructions, the carbon appears heterogeneous
and porous below and above each NP. This is probably due to the non-linear
intensity in ADF images (diffraction contrast). In contrast, DIP-TV retrieves
near-spherical NPs and a homogeneous carbon support, under all acquisition
conditions. Using 20° increment (7 projections in total), the shape of the
carbon is slightly distorted on the right-hand side, but the technique largely
outperfoms SIRT and CS-TV.

Conclusion

This work shows the robustness of DIP-TV for ET using a limited number of
projections and a restricted tilt range. The method benefits from the power of
neural network architecture, but requires no training data set, making it
suitable for ET and extremely versatile since it can be used under different
acquisition conditions. Moreover, the method could be applied to different
modalities of the same material and potentially directly for 3D reconstruction.
**Graphic:**

<figure><img src="image_2.png" /></figure>

**Keywords:**

Electron Tomography, Reconstruction, Deep Learning

**Reference:**

M. Jacob et al., Ultramicroscopy 2021, 225:113289.

Y. Jiang et al., Ultramicroscopy 2018, 186:94.

D. Ulyanov et al., International journal of computer vision 2020, 128:1867.

D. Baguer, et al., Inverse Problems 2020, 36.9:094004.

This work, carried out on the Platform for Nanocharacterisation (PFNC), was supported by the "Recherche Technologique de Base" and "France 2030 - ANR-22-PEEL-0014" programs of the French National Research Agency (ANR).