Neutron Tomo

Neutron Radiography / 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
🥇 PETFormer 0.813 34.79 0.966 ✓ Certified Li et al., ECCV 2024
🥈 TransEM 0.781 33.7 0.938 ✓ Certified Xie et al., 2023
🥉 DeepPET 0.749 32.4 0.918 ✓ Certified Haggstrom et al., MIA 2019
4 PET-ViT 0.724 30.63 0.926 ✓ Certified Smith et al., ICCV 2024
5 U-Net-PET 0.722 30.59 0.925 ✓ Certified Ronneberger et al. variant, MICCAI 2020
6 MAPEM-RDP 0.632 28.5 0.815 ✓ Certified Nuyts et al., 2002
7 FBP-PET 0.628 26.95 0.857 ✓ Certified Analytical baseline
8 ML-EM 0.588 25.64 0.822 ✓ Certified Shepp & Vardi, IEEE TPAMI 1982
9 OS-EM 0.542 24.21 0.776 ✓ Certified Hudson & Larkin, IEEE TMI 1994
10 OSEM 0.508 24.8 0.690 ✓ Certified Hudson & Larkin, IEEE TMI 1994

Dataset: PWM Benchmark (10 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
🥇 PETFormer + gradient 0.731
0.804
33.69 dB / 0.958
0.724
28.79 dB / 0.896
0.666
26.06 dB / 0.834
✓ Certified Li et al., ECCV 2024
🥈 TransEM + gradient 0.655
0.764
31.28 dB / 0.934
0.642
24.97 dB / 0.801
0.560
22.45 dB / 0.709
✓ Certified Xie et al., 2023
🥉 DeepPET + gradient 0.636
0.769
31.02 dB / 0.931
0.618
24.36 dB / 0.781
0.520
21.07 dB / 0.649
✓ Certified Haggstrom et al., MIA 2019
4 FBP-PET + gradient 0.635
0.673
25.84 dB / 0.827
0.636
25.07 dB / 0.804
0.596
23.92 dB / 0.766
✓ Certified Analytical baseline
5 U-Net-PET + gradient 0.615
0.719
28.7 dB / 0.895
0.600
23.37 dB / 0.745
0.526
21.08 dB / 0.649
✓ Certified Ronneberger et al. variant, MICCAI 2020
6 PET-ViT + gradient 0.604
0.717
28.47 dB / 0.890
0.605
23.99 dB / 0.768
0.491
19.24 dB / 0.562
✓ Certified Smith et al., ICCV 2024
7 MAPEM-RDP + gradient 0.569
0.679
26.58 dB / 0.848
0.562
21.94 dB / 0.687
0.465
18.45 dB / 0.522
✓ Certified Nuyts et al., IEEE TMI 2002
8 ML-EM + gradient 0.559
0.602
22.99 dB / 0.731
0.557
21.59 dB / 0.672
0.519
20.4 dB / 0.618
✓ Certified Shepp & Vardi, IEEE TPAMI 1982
9 OS-EM + gradient 0.530
0.603
22.71 dB / 0.720
0.515
20.46 dB / 0.621
0.472
19.15 dB / 0.557
✓ Certified Hudson & Larkin, IEEE TMI 1994
10 OSEM + gradient 0.523
0.594
22.99 dB / 0.731
0.504
19.75 dB / 0.587
0.471
18.7 dB / 0.535
✓ Certified Hudson & Larkin, IEEE TMI 1994

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 PETFormer + gradient 0.804 33.69 0.958
2 DeepPET + gradient 0.769 31.02 0.931
3 TransEM + gradient 0.764 31.28 0.934
4 U-Net-PET + gradient 0.719 28.7 0.895
5 PET-ViT + gradient 0.717 28.47 0.89
6 MAPEM-RDP + gradient 0.679 26.58 0.848
7 FBP-PET + gradient 0.673 25.84 0.827
8 OS-EM + gradient 0.603 22.71 0.72
9 ML-EM + gradient 0.602 22.99 0.731
10 OSEM + gradient 0.594 22.99 0.731
Spec Ranges (3 parameters)
Parameter Min Max Unit
beam_spectrum -3.0 6.0 %
scatter_correction -5.0 10.0 %
rotation_offset -1.0 2.0 pixels
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 PETFormer + gradient 0.724 28.79 0.896
2 TransEM + gradient 0.642 24.97 0.801
3 FBP-PET + gradient 0.636 25.07 0.804
4 DeepPET + gradient 0.618 24.36 0.781
5 PET-ViT + gradient 0.605 23.99 0.768
6 U-Net-PET + gradient 0.600 23.37 0.745
7 MAPEM-RDP + gradient 0.562 21.94 0.687
8 ML-EM + gradient 0.557 21.59 0.672
9 OS-EM + gradient 0.515 20.46 0.621
10 OSEM + gradient 0.504 19.75 0.587
Spec Ranges (3 parameters)
Parameter Min Max Unit
beam_spectrum -3.6 5.4 %
scatter_correction -6.0 9.0 %
rotation_offset -1.2 1.8 pixels
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 PETFormer + gradient 0.666 26.06 0.834
2 FBP-PET + gradient 0.596 23.92 0.766
3 TransEM + gradient 0.560 22.45 0.709
4 U-Net-PET + gradient 0.526 21.08 0.649
5 DeepPET + gradient 0.520 21.07 0.649
6 ML-EM + gradient 0.519 20.4 0.618
7 PET-ViT + gradient 0.491 19.24 0.562
8 OS-EM + gradient 0.472 19.15 0.557
9 OSEM + gradient 0.471 18.7 0.535
10 MAPEM-RDP + gradient 0.465 18.45 0.522
Spec Ranges (3 parameters)
Parameter Min Max Unit
beam_spectrum -2.1 6.9 %
scatter_correction -3.5 11.5 %
rotation_offset -0.7 2.3 pixels
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

Neutron imaging exploits the unique interaction of thermal neutrons with matter — neutrons are attenuated strongly by light elements (hydrogen, lithium, boron) while penetrating heavy elements (lead, iron) that are opaque to X-rays. The forward model follows Beer-Lambert: I = I_0 * exp(-integral(Sigma(s) ds)) where Sigma is the macroscopic cross-section. Tomographic reconstruction from multiple projection angles uses FBP or iterative methods. Neutron sources include research reactors and spallation sources. The lower flux compared to X-rays requires longer exposures (seconds) and results in lower spatial resolution (50-100 um).

Principle

Neutron radiography and tomography image the transmission of a thermal or cold neutron beam through a sample. Neutrons interact with nuclei (not electrons), providing complementary contrast to X-rays: hydrogen-rich materials (water, polymers, organics) attenuate neutrons strongly, while metals like aluminum and lead are relatively transparent. Tomographic reconstruction from multiple projection angles yields 3-D maps of neutron attenuation.

How to Build the System

Access a research reactor or spallation neutron source with an imaging beamline (e.g., ICON at PSI, IMAT at ISIS, NIST BT-2). A collimated neutron beam (thermal or cold, 1-10 Å) passes through the sample, and a scintillator-camera system (⁶LiF/ZnS screen + sCMOS camera) records the transmitted intensity. Rotate the sample through 180° or 360° for tomography. Spatial resolution is typically 20-100 μm, limited by beam divergence and scintillator thickness.

Common Reconstruction Algorithms

  • Filtered back-projection (FBP) adapted for neutron tomography
  • Iterative reconstruction (SIRT, CGLS) for limited-angle or noisy data
  • Beam hardening correction for polychromatic neutron spectra
  • Scattering correction (point-scattered function approach)
  • Neutron phase-contrast tomography (grating interferometry)

Common Mistakes

  • Scattering from hydrogen-rich samples producing artifacts (halo around sample)
  • Beam hardening (spectral hardening) not corrected for polychromatic beams
  • Activation of sample materials, creating radiation safety issues post-experiment
  • Gamma contamination in the beam degrading image quality
  • Insufficient exposure time per projection, yielding noisy tomograms

How to Avoid Mistakes

  • Apply scattering correction algorithms; use thin or diluted hydrogen-rich samples
  • Correct beam hardening with polynomial methods or by using a velocity selector (monochromatic)
  • Check sample activation potential before irradiation; use short-lived isotope-free materials
  • Use gamma-blind detectors (⁶Li glass) or filters to reject gamma contamination
  • Optimize exposure per projection for adequate SNR; total scan time often 2-8 hours

Forward-Model Mismatch Cases

  • The widefield fallback applies optical Gaussian blur, but neutron tomography measures neutron transmission (I = I_0 * exp(-sigma_t * n * t)) — neutrons interact with nuclei, not electron clouds, giving completely different contrast (hydrogen-rich materials are opaque to neutrons but transparent to X-rays)
  • Neutron attenuation depends on nuclear cross-sections that vary dramatically between isotopes (H, Li, B are strong absorbers) — the widefield model has no nuclear physics and cannot distinguish materials by their neutron interaction properties

How to Correct the Mismatch

  • Use the neutron tomography operator implementing Beer-Lambert neutron transmission: y(theta,s) = I_0 * exp(-integral(Sigma_t(x,y) dl)) where Sigma_t is the macroscopic total cross-section
  • Reconstruct using FBP or iterative methods (same algorithms as X-ray CT) but with neutron-specific attenuation coefficients — neutron imaging reveals hydrogen/water content, lithium batteries, and metallurgical features invisible to X-rays

Experimental Setup — Signal Chain

Experimental setup diagram for Neutron Radiography / Tomography

Experimental Setup

Instrument: PSI ICON beamline / NIST BT-2 / ORNL CG-1D
Neutron Energy Ev: 0.025
Energy Type: thermal
Detector: LiF/ZnS scintillator + CCD
Pixel Size Um: 100
Image Size: 2048x2048
Exposure S: 10
Flux N Per Cm2 S: 100000000.0
Facility: research reactor / spallation source

Key References

  • Kardjilov et al., 'Advances in neutron imaging', Materials Today 21, 652-672 (2018)
  • IAEA, 'Neutron Imaging: A Non-Destructive Tool for Materials Testing', IAEA-TECDOC-1604 (2008)

Canonical Datasets

  • PSI ICON neutron imaging benchmark data
  • NIST neutron radiography reference images

Spec DAG — Forward Model Pipeline

R(θ) → Π(neutron) → D(g, η₁)

R Sample Rotation (θ)
Π Neutron Attenuation Projection (neutron)
D Scintillator + CCD (g, η₁)

Mismatch Parameters

Symbol Parameter Description Nominal Perturbed
ΔE beam_spectrum Beam energy spectrum error (%) 0 3.0
Δs scatter_correction Scatter correction error (%) 0 5.0
Δθ rotation_offset Rotation center offset (pixels) 0 1.0

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.