Electron Tomo

Electron Tomography

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Standard reconstruction benchmark — forward model perfectly known, no calibration needed. Score = 0.5 × clip((PSNR−15)/30, 0, 1) + 0.5 × SSIM

# Method Score PSNR (dB) SSIM Source
🥇 DiffET 0.878 39.1 0.952 ✓ Certified Gao et al. 2024
🥈 PhysET 0.848 37.7 0.940 ✓ Certified Chen et al. 2024
🥉 SwinET 0.821 36.4 0.929 ✓ Certified Wang et al. 2023
4 TransET 0.785 34.8 0.910 ✓ Certified Li et al. 2022
5 IsoNet 0.721 32.1 0.871 ✓ Certified Liu et al. 2021
6 DnCNN-ET 0.653 29.3 0.829 ✓ Certified Buchholz et al. 2019
7 CS-ET 0.575 26.4 0.769 ✓ Certified Leary et al. 2013
8 SIRT-ET 0.505 23.6 0.724 ✓ Certified Gilbert 1972
9 WBP-ET 0.437 20.9 0.678 ✓ Certified Radermacher et al. 1987

Dataset: PWM Benchmark (9 algorithms)

Blind Reconstruction Challenge — forward model has unknown mismatch, must calibrate from data. Score = 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖)

# Method Overall Score Public
PSNR / SSIM
 Dev
PSNR / SSIM
 Hidden
PSNR / SSIM
 Trust Source
🥇 DiffET + gradient 0.764
0.834
36.57 dB / 0.976
0.753
31.33 dB / 0.935
0.706
29.0 dB / 0.900
✓ Certified Gao et al., NeurIPS 2024
🥈 SwinET + gradient 0.763
0.803
34.36 dB / 0.963
0.754
30.95 dB / 0.930
0.732
29.47 dB / 0.908
✓ Certified Wang et al., Ultramicroscopy 2023
🥉 PhysET + gradient 0.714
0.839
36.16 dB / 0.974
0.685
26.79 dB / 0.853
0.619
24.74 dB / 0.794
✓ Certified Chen et al., Nat. Commun. 2024
4 TransET + gradient 0.704
0.802
33.4 dB / 0.956
0.715
28.69 dB / 0.895
0.594
23.08 dB / 0.734
✓ Certified Li et al., Nat. Methods 2022
5 IsoNet + gradient 0.660
0.768
31.1 dB / 0.932
0.624
24.11 dB / 0.772
0.588
23.53 dB / 0.751
✓ Certified Liu et al., Nat. Commun. 2021
6 DnCNN-ET + gradient 0.610
0.691
27.07 dB / 0.860
0.587
22.47 dB / 0.710
0.552
21.34 dB / 0.661
✓ Certified Buchholz et al., Nat. Methods 2019
7 SIRT-ET + gradient 0.554
0.591
22.41 dB / 0.707
0.562
21.91 dB / 0.686
0.508
20.56 dB / 0.625
✓ Certified Gilbert, J. Theor. Biol. 1972
8 CS-ET + gradient 0.455
0.617
23.49 dB / 0.750
0.409
16.9 dB / 0.445
0.338
14.0 dB / 0.310
✓ Certified Leary et al., Ultramicroscopy 2013
9 WBP-ET + gradient 0.417
0.460
17.91 dB / 0.496
0.410
17.12 dB / 0.456
0.382
16.17 dB / 0.410
✓ Certified Radermacher et al., J. Microsc. 1987

Complete score requires all 3 tiers (Public + Dev + Hidden).

Join the competition →
Scoring: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖) PSNR 40% · SSIM 40% · Consistency 20%
Public 3 scenes

Full-access development tier with all data visible.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), spec ranges, ground truth (x_true), and true mismatch spec.

How to use: Load HDF5 → compare reconstruction vs x_true → check consistency → iterate.

What to submit: Reconstructed signals (x_hat) and corrected spec as HDF5.

Public Leaderboard
# Method Score PSNR SSIM
1 PhysET + gradient 0.839 36.16 0.974
2 DiffET + gradient 0.834 36.57 0.976
3 SwinET + gradient 0.803 34.36 0.963
4 TransET + gradient 0.802 33.4 0.956
5 IsoNet + gradient 0.768 31.1 0.932
6 DnCNN-ET + gradient 0.691 27.07 0.86
7 CS-ET + gradient 0.617 23.49 0.75
8 SIRT-ET + gradient 0.591 22.41 0.707
9 WBP-ET + gradient 0.460 17.91 0.496
Spec Ranges (3 parameters)
Parameter Min Max Unit
tilt_angle -0.5 1.0 deg
tilt_axis -0.3 0.6 deg
defocus_gradient -10.0 20.0 nm/μm
View Details →
Dev 3 scenes

Blind evaluation tier — no ground truth available.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), and spec ranges only.

How to use: Apply your pipeline from the Public tier. Use consistency as self-check.

What to submit: Reconstructed signals and corrected spec. Scored server-side.

Dev Leaderboard
# Method Score PSNR SSIM
1 SwinET + gradient 0.754 30.95 0.93
2 DiffET + gradient 0.753 31.33 0.935
3 TransET + gradient 0.715 28.69 0.895
4 PhysET + gradient 0.685 26.79 0.853
5 IsoNet + gradient 0.624 24.11 0.772
6 DnCNN-ET + gradient 0.587 22.47 0.71
7 SIRT-ET + gradient 0.562 21.91 0.686
8 WBP-ET + gradient 0.410 17.12 0.456
9 CS-ET + gradient 0.409 16.9 0.445
Spec Ranges (3 parameters)
Parameter Min Max Unit
tilt_angle -0.6 0.9 deg
tilt_axis -0.36 0.54 deg
defocus_gradient -12.0 18.0 nm/μm
Submit Reconstruction View Details →
Hidden 3 scenes

Fully blind server-side evaluation — no data download.

What you get & how to use

What you get: No data downloadable. Algorithm runs server-side on hidden measurements.

How to use: Package algorithm as Docker container / Python script. Submit via link.

What to submit: Containerized algorithm accepting y + H, outputting x_hat + corrected spec.

Hidden Leaderboard
# Method Score PSNR SSIM
1 SwinET + gradient 0.732 29.47 0.908
2 DiffET + gradient 0.706 29.0 0.9
3 PhysET + gradient 0.619 24.74 0.794
4 TransET + gradient 0.594 23.08 0.734
5 IsoNet + gradient 0.588 23.53 0.751
6 DnCNN-ET + gradient 0.552 21.34 0.661
7 SIRT-ET + gradient 0.508 20.56 0.625
8 WBP-ET + gradient 0.382 16.17 0.41
9 CS-ET + gradient 0.338 14.0 0.31
Spec Ranges (3 parameters)
Parameter Min Max Unit
tilt_angle -0.35 1.15 deg
tilt_axis -0.21 0.69 deg
defocus_gradient -7.0 23.0 nm/μm
Submit Algorithm View Details →

Blind Reconstruction Challenge

Challenge

Given measurements with unknown mismatch and spec ranges (not exact params), reconstruct the original signal. A method must be evaluated on all three tiers for a complete score. Scored on a composite metric: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖).

Input

Measurements y, ideal forward model H, spec ranges

Output

Reconstructed signal x̂

About the Imaging Modality

Electron tomography reconstructs 3D structure from a tilt series of 2D projections acquired as the specimen is rotated (+/-60-70 deg, 1-2 deg increments). The missing wedge of angular coverage causes elongation artifacts along the beam direction. Alignment of the tilt series (using fiducial gold markers or cross-correlation) is critical. Reconstruction uses WBP, SIRT, or compressed sensing methods with TV priors to mitigate missing-wedge artifacts.

Principle

Electron tomography reconstructs a 3-D volume from a tilt series of 2-D TEM or STEM projections acquired at different specimen tilts (typically ±60-70°). The Radon transform (or its generalization) relates the projections to the 3-D structure. The limited tilt range causes a 'missing wedge' artifact — elongation in the beam direction — which must be addressed by regularization or dual-axis acquisition.

How to Build the System

Use a TEM/STEM with a high-tilt specimen holder (±70-80°). Acquire images at tilt increments of 1-2° across the full range. For STEM tomography, HAADF signal provides monotonic contrast (no CTF complications). Include gold nanoparticles as fiducial markers for alignment. Automated acquisition software (SerialEM, Tomography by Thermo Fisher) controls stage tilt, focus tracking, and image acquisition.

Common Reconstruction Algorithms

  • Weighted back-projection (WBP)
  • SIRT / SART (Simultaneous Iterative Reconstruction Techniques)
  • GENFIRE (GENeralized Fourier Iterative REconstruction)
  • Compressed sensing tomography for missing-wedge artifact reduction
  • Deep-learning tomographic reconstruction (TomoGAN, DeepRecon)

Common Mistakes

  • Poor tilt-series alignment causing blurring in the reconstruction
  • Missing wedge artifacts not addressed, distorting features along the beam axis
  • Specimen drift or deformation during the tilt series (especially for biological specimens)
  • Dose damage accumulating through the tilt series degrading later images
  • Inaccurate tilt angles due to stage mechanical backlash

How to Avoid Mistakes

  • Align tilt series carefully using fiducial markers; refine with cross-correlation
  • Use dual-axis tomography or compressed-sensing reconstruction to fill the missing wedge
  • Apply autofocus and drift tracking at each tilt; use cryo-conditions for biology
  • Distribute dose evenly; start at high tilts where damage impact is greatest
  • Calibrate stage tilt angle accuracy; use Saxton scheme (non-linear tilt increments)

Forward-Model Mismatch Cases

  • The widefield fallback processes only 2D (64,64) images, but electron tomography acquires a tilt series — projections at multiple angles through the 3D specimen volume, with output shape (n_tilts, H, W)
  • The missing wedge problem (limited tilt range, typically +/- 70 degrees) is specific to electron tomography and cannot be modeled by the widefield operator — reconstructions without accounting for missing data have severe elongation artifacts

How to Correct the Mismatch

  • Use the electron tomography operator that generates projection images at each tilt angle via the Radon transform applied to the 3D specimen density, including the limited tilt range constraint
  • Reconstruct using weighted back-projection (WBP), SIRT, or compressed-sensing methods that account for the missing wedge and alignment errors between tilt images

Experimental Setup — Signal Chain

Experimental setup diagram for Electron Tomography

Experimental Setup

Instrument: Thermo Fisher Titan Krios G4 / JEOL JEM-2200FS
Accelerating Voltage Kv: 200
Tilt Range Deg: [-70, 70]
Tilt Increment Deg: 2.0
Number Of Projections: 71
Detector: HAADF-STEM / Gatan K3
Pixel Size Nm: 0.71
Total Dose E Per Nm2: 39000
Reconstruction: SIRT / WBP

Key References

  • Frank, 'Electron Tomography', Springer (2006)
  • Midgley & Dunin-Borkowski, 'Electron tomography and holography in materials science', Nature Materials 8, 271 (2009)

Canonical Datasets

  • EMPIAR cryo-ET tilt series (e.g., EMPIAR-10045)
  • ETDB (Electron Tomography Database, Caltech)

Spec DAG — Forward Model Pipeline

R(θ) → P(e⁻) → Π(proj) → D(g, η₁)

R Sample Tilt (θ)
P Electron Wave (e⁻)
Π Projection (proj)
D Detector (g, η₁)

Mismatch Parameters

Symbol Parameter Description Nominal Perturbed
Δθ tilt_angle Tilt angle error (deg) 0 0.5
Δφ tilt_axis Tilt axis misalignment (deg) 0 0.3
Δf' defocus_gradient Defocus gradient (nm/μm) 0 10

Credits System

40%
Platform Profit Pool
Revenue allocated to benchmark rewards
30%
Winner Share
Top algorithm receives from pool
$100
Min Withdrawal
Minimum payout threshold
Spec Primitives Reference (11 primitives)
P Propagation

Free-space or medium propagation kernel (Fresnel, Rayleigh-Sommerfeld).

M Mask / Modulation

Spatial or spatio-temporal amplitude modulation (coded aperture, SLM pattern).

Π Projection

Geometric projection operator (Radon transform, fan-beam, cone-beam).

F Fourier Sampling

Sampling in the Fourier / k-space domain (MRI, ptychography).

C Convolution

Shift-invariant convolution with a point-spread function (PSF).

Σ Summation / Integration

Summation along a physical dimension (spectral, temporal, angular).

D Detector

Sensor readout with gain g and noise model η (Gaussian, Poisson, mixed).

S Structured Illumination

Patterned illumination (block, Hadamard, random) applied to the scene.

W Wavelength Dispersion

Spectral dispersion element (prism, grating) with shift α and aperture a.

R Rotation / Motion

Sample or gantry rotation (CT, electron tomography).

Λ Wavelength Selection

Spectral filter or monochromator selecting a wavelength band.