Proton Radiography

Proton Radiography

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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
🥇 pCT-Former 0.760 33.0 0.920 ✓ Certified Proton CT transformer, 2024
🥈 ProtonNet 0.712 31.0 0.890 ✓ Certified Proton CT DL, 2022
🥉 DROP-TVS 0.595 27.0 0.790 ✓ Certified Penfold et al., 2010
4 FBP-MLP 0.467 23.5 0.650 ✓ Certified Schulte et al., 2008

Dataset: PWM Benchmark (4 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
🥇 pCT-Former + gradient 0.710
0.751
30.15 dB / 0.919
0.709
28.05 dB / 0.882
0.670
27.11 dB / 0.861
✓ Certified Proton CT transformer, 2024
🥈 ProtonNet + gradient 0.584
0.718
28.28 dB / 0.887
0.536
21.42 dB / 0.665
0.497
19.92 dB / 0.595
✓ Certified Proton CT DL reconstruction, 2022
🥉 DROP-TVS + gradient 0.575
0.674
25.85 dB / 0.828
0.553
21.26 dB / 0.657
0.498
20.07 dB / 0.602
✓ Certified Penfold et al., Med. Phys. 2010
4 FBP-MLP + gradient 0.537
0.547
20.95 dB / 0.643
0.534
21.15 dB / 0.652
0.529
20.9 dB / 0.641
✓ Certified Schulte et al., Med. Phys. 2008

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 pCT-Former + gradient 0.751 30.15 0.919
2 ProtonNet + gradient 0.718 28.28 0.887
3 DROP-TVS + gradient 0.674 25.85 0.828
4 FBP-MLP + gradient 0.547 20.95 0.643
Spec Ranges (3 parameters)
Parameter Min Max Unit
energy_loss -2.0 4.0 %
scattering -5.0 10.0 %
range_straggling -3.0 6.0 %
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 pCT-Former + gradient 0.709 28.05 0.882
2 DROP-TVS + gradient 0.553 21.26 0.657
3 ProtonNet + gradient 0.536 21.42 0.665
4 FBP-MLP + gradient 0.534 21.15 0.652
Spec Ranges (3 parameters)
Parameter Min Max Unit
energy_loss -2.4 3.6 %
scattering -6.0 9.0 %
range_straggling -3.6 5.4 %
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 pCT-Former + gradient 0.670 27.11 0.861
2 FBP-MLP + gradient 0.529 20.9 0.641
3 DROP-TVS + gradient 0.498 20.07 0.602
4 ProtonNet + gradient 0.497 19.92 0.595
Spec Ranges (3 parameters)
Parameter Min Max Unit
energy_loss -1.4 4.6 %
scattering -3.5 11.5 %
range_straggling -2.1 6.9 %
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

Proton radiography/CT uses high-energy proton beams (100-250 MeV) to image the relative stopping power (RSP) of tissue, which is the quantity directly needed for proton therapy treatment planning. Unlike X-rays which measure attenuation, proton imaging measures the energy loss and scattering of individual protons as they traverse the object. Each proton's entry/exit position and angle are tracked, and the residual energy is measured. The RSP is reconstructed from many proton histories using iterative algorithms. Challenges include multiple Coulomb scattering (which blurs the spatial resolution to ~1 mm) and the need for single-proton tracking at high rates.

Principle

Proton radiography images the transmission and scattering of high-energy protons (50-800 MeV) through dense objects. Unlike X-rays, protons undergo significant multiple Coulomb scattering (MCS) in matter, which provides density and compositional contrast. Both transmission (energy loss) and scattering angle measurements contribute to image formation. Proton radiography can penetrate very dense materials (steel, depleted uranium) that are opaque to X-rays.

How to Build the System

Requires a high-energy proton accelerator facility (synchrotron or cyclotron delivering 200-800 MeV protons). The object is placed in the beam path between tracking detectors (silicon strip or GEM detectors) that measure each proton's position and angle before and after the object. A magnetic spectrometer (quadrupole lens system, e.g., at LANL pRad facility) focuses transmitted protons onto a scintillator + camera detector.

Common Reconstruction Algorithms

  • Most Likely Path (MLP) estimation for proton CT reconstruction
  • Filtered back-projection with scattering-angle weighting
  • Algebraic reconstruction (ART) with MCS forward model
  • Material discrimination from dual-parameter (transmission + scattering) analysis
  • Deep-learning proton CT reconstruction for reduced view angles

Common Mistakes

  • Ignoring multiple Coulomb scattering in the reconstruction model, causing blur
  • Nuclear interaction losses (protons stopped or scattered out of detector acceptance)
  • Insufficient proton statistics leading to noisy images
  • Energy straggling not modeled, causing depth-of-field blur in radiography
  • Detector alignment errors between upstream and downstream tracking systems

How to Avoid Mistakes

  • Use MLP or cubic spline path estimation in iterative reconstruction algorithms
  • Account for nuclear interaction losses in the forward model; filter outlier tracks
  • Accumulate sufficient proton histories (>10⁶ for radiography, >10⁸ for proton CT)
  • Include energy straggling in the forward model or use higher energy protons to reduce it
  • Carefully align tracking detectors with survey or use track-based alignment algorithms

Forward-Model Mismatch Cases

  • The widefield fallback applies Gaussian blur, but proton radiography measures energy loss and multiple Coulomb scattering (MCS) of high-energy protons traversing the object — the scattering angle distribution encodes areal density, not spatial blur
  • Protons lose energy continuously (Bethe-Bloch formula: -dE/dx ~ Z/A * z^2/beta^2) and scatter via Coulomb interaction — the measurement combines transmission intensity, residual energy, and scattering angle, none of which are modeled by optical blur

How to Correct the Mismatch

  • Use the proton radiography operator that models energy-dependent proton transport: energy loss via Bethe-Bloch stopping power and angular broadening via Highland MCS formula (theta_rms ~ 13.6 MeV/(p*v) * sqrt(t/X_0))
  • Reconstruct water-equivalent path length (WEPL) maps from residual energy measurements, or use scattering radiography for material discrimination — essential for proton therapy treatment planning

Experimental Setup — Signal Chain

Experimental setup diagram for Proton Radiography

Experimental Setup

Instrument: Phase-II proton CT prototype (Loma Linda / NIU)
Proton Energy Mev: 200
Detector: scintillating fiber tracker + residual energy calorimeter
Tracker Planes: 4
Image Matrix: 256x256
Projections: 360
Rsp Accuracy Percent: 1.0
Application: proton therapy treatment planning verification

Key References

  • Schulte et al., 'Conceptual design of a proton computed tomography system for applications in proton radiation therapy', IEEE Trans. Nucl. Sci. 51, 866-872 (2004)

Canonical Datasets

  • Simulated proton CT phantoms (Penfold et al.)

Spec DAG — Forward Model Pipeline

Π(proton) → D(g, η₁)

Π Proton Transmission (proton)
D Tracking Detector (g, η₁)

Mismatch Parameters

Symbol Parameter Description Nominal Perturbed
ΔS energy_loss Stopping power error (%) 0 2.0
Δθ_MCS scattering Multiple Coulomb scattering error (%) 0 5.0
ΔR range_straggling Range straggling error (%) 0 3.0

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.