Atom Probe Tomography (APT)

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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
🥇	EquivAPT EquivAPT Equivariant atom probe transformer, 2025 36.3 dB SSIM 0.948 Checkpoint unavailable	0.829	36.3	0.948	✓ Certified	Equivariant atom probe transformer, 2025
🥈	DiffusionAPT DiffusionAPT Adapted: Chung et al., ICLR 2023 35.1 dB SSIM 0.934 Checkpoint unavailable	0.802	35.1	0.934	✓ Certified	Adapted: Chung et al., ICLR 2023
🥉	APT-Former APT-Former Moody et al., Microsc. Microanal. 30(2):341, 2024 33.6 dB SSIM 0.912 Checkpoint unavailable	0.766	33.6	0.912	✓ Certified	Moody et al., Microsc. Microanal. 30(2):341, 2024
4	TrajectoryPINN TrajectoryPINN De Geuser & Gault, Annu. Rev. Mater. Res. 52:1, 2022 31.2 dB SSIM 0.876 Checkpoint unavailable	0.708	31.2	0.876	✓ Certified	De Geuser & Gault, Annu. Rev. Mater. Res. 52:1, 2022
5	LISTA-APT LISTA-APT Gregor & LeCun ICML 2010; adapted APT 2020 29.5 dB SSIM 0.842 Checkpoint unavailable	0.663	29.5	0.842	✓ Certified	Gregor & LeCun ICML 2010; adapted APT 2020
6	ResNet-ArtefactCorr ResNet-ArtefactCorr Wei et al., Ultramicroscopy 206:112817, 2019 28.7 dB SSIM 0.818 Checkpoint unavailable	0.637	28.7	0.818	✓ Certified	Wei et al., Ultramicroscopy 206:112817, 2019
7	PnP-BM3D (APT) PnP-BM3D (APT) Danielyan et al., IEEE TIP 21(9):3884, 2012 26.1 dB SSIM 0.750 Try in SpecLab →	0.560	26.1	0.750	✓ Certified	Danielyan et al., IEEE TIP 21(9):3884, 2012
8	Tikhonov-Trajectory Tikhonov-Trajectory Geiser et al., Microsc. Microanal. 13(6):437, 2007 23.4 dB SSIM 0.660 Try in SpecLab →	0.470	23.4	0.660	✓ Certified	Geiser et al., Microsc. Microanal. 13(6):437, 2007
9	Bas-Protocol Bas-Protocol Bas et al., Appl. Surf. Sci. 87-88:298, 1995 20.8 dB SSIM 0.550 Try in SpecLab →	0.372	20.8	0.550	✓ Certified	Bas et al., Appl. Surf. Sci. 87-88:298, 1995

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
🥇	EquivAPT + gradient EquivAPT + gradient Adapted from equivariant vision transformer for atomic imaging, 2025 Score 0.766 Correct & Reconstruct →	0.766	0.799 33.42 dB / 0.956	0.766 31.76 dB / 0.940	0.734 30.87 dB / 0.929	✓ Certified	Adapted from equivariant vision transformer for atomic imaging, 2025
🥈	DiffusionAPT + gradient DiffusionAPT + gradient Inspired by Chung et al., ICLR 2023 (score-based MRI) Score 0.736 Correct & Reconstruct →	0.736	0.807 33.75 dB / 0.959	0.716 29.31 dB / 0.906	0.684 26.95 dB / 0.857	✓ Certified	Inspired by Chung et al., ICLR 2023 (score-based MRI)
🥉	APT-Former + gradient APT-Former + gradient Moody et al., Microsc. Microanal. 30(2):341, 2024 Score 0.693 Correct & Reconstruct →	0.693	0.759 30.67 dB / 0.926	0.707 28.25 dB / 0.886	0.613 24.5 dB / 0.786	✓ Certified	Moody et al., Microsc. Microanal. 30(2):341, 2024
4	TrajectoryPINN + gradient TrajectoryPINN + gradient De Geuser & Gault, Annu. Rev. Mater. Res. 52:1, 2022 Score 0.638 Correct & Reconstruct →	0.638	0.726 28.88 dB / 0.898	0.624 24.67 dB / 0.792	0.565 21.81 dB / 0.682	✓ Certified	De Geuser & Gault, Annu. Rev. Mater. Res. 52:1, 2022
5	LISTA-APT + gradient LISTA-APT + gradient Gregor & LeCun, ICML 2010; adapted for APT 2020 Score 0.599 Correct & Reconstruct →	0.599	0.694 27.23 dB / 0.864	0.590 22.91 dB / 0.728	0.513 20.46 dB / 0.621	✓ Certified	Gregor & LeCun, ICML 2010; adapted for APT 2020
6	ResNet-ArtefactCorr + gradient ResNet-ArtefactCorr + gradient Wei et al., Ultramicroscopy 206:112817, 2019 Score 0.573 Correct & Reconstruct →	0.573	0.682 26.77 dB / 0.852	0.543 20.87 dB / 0.640	0.495 19.37 dB / 0.568	✓ Certified	Wei et al., Ultramicroscopy 206:112817, 2019
7	Tikhonov-Trajectory + gradient Tikhonov-Trajectory + gradient Geiser et al., Microsc. Microanal. 13(6):437, 2007 Score 0.534 Correct & Reconstruct →	0.534	0.547 21.02 dB / 0.647	0.539 21.31 dB / 0.660	0.515 20.67 dB / 0.630	✓ Certified	Geiser et al., Microsc. Microanal. 13(6):437, 2007
8	PnP-BM3D (APT) + gradient PnP-BM3D (APT) + gradient Danielyan et al., IEEE TIP 21(9):3884, 2012 Score 0.502 Correct & Reconstruct →	0.502	0.624 24.1 dB / 0.772	0.494 19.15 dB / 0.557	0.387 16.56 dB / 0.428	✓ Certified	Danielyan et al., IEEE TIP 21(9):3884, 2012
9	Bas-Protocol + gradient Bas-Protocol + gradient Bas et al., Appl. Surf. Sci. 87-88:298, 1995 Score 0.459 Correct & Reconstruct →	0.459	0.514 19.67 dB / 0.583	0.453 18.29 dB / 0.514	0.411 17.18 dB / 0.459	✓ Certified	Bas et al., Appl. Surf. Sci. 87-88:298, 1995

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

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Scoring: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖) PSNR 40% · SSIM 40% · Consistency 20%

Public 5 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	DiffusionAPT + gradient	0.807	33.75	0.959
2	EquivAPT + gradient	0.799	33.42	0.956
3	APT-Former + gradient	0.759	30.67	0.926
4	TrajectoryPINN + gradient	0.726	28.88	0.898
5	LISTA-APT + gradient	0.694	27.23	0.864
6	ResNet-ArtefactCorr + gradient	0.682	26.77	0.852
7	PnP-BM3D (APT) + gradient	0.624	24.1	0.772
8	Tikhonov-Trajectory + gradient	0.547	21.02	0.647
9	Bas-Protocol + gradient	0.514	19.67	0.583

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
flight_path_error	-0.1	0.2	mm
voltage_calibration	0.996	1.008	-
detection_efficiency	0.58	0.64	-
tip_radius_error	-1.0	2.0	nm

View Details →

Dev 5 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	EquivAPT + gradient	0.766	31.76	0.94
2	DiffusionAPT + gradient	0.716	29.31	0.906
3	APT-Former + gradient	0.707	28.25	0.886
4	TrajectoryPINN + gradient	0.624	24.67	0.792
5	LISTA-APT + gradient	0.590	22.91	0.728
6	ResNet-ArtefactCorr + gradient	0.543	20.87	0.64
7	Tikhonov-Trajectory + gradient	0.539	21.31	0.66
8	PnP-BM3D (APT) + gradient	0.494	19.15	0.557
9	Bas-Protocol + gradient	0.453	18.29	0.514

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
flight_path_error	-0.12	0.18	mm
voltage_calibration	0.9952	1.0072	-
detection_efficiency	0.576	0.636	-
tip_radius_error	-1.2	1.8	nm

Submit Reconstruction View Details →

Hidden 5 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	EquivAPT + gradient	0.734	30.87	0.929
2	DiffusionAPT + gradient	0.684	26.95	0.857
3	APT-Former + gradient	0.613	24.5	0.786
4	TrajectoryPINN + gradient	0.565	21.81	0.682
5	Tikhonov-Trajectory + gradient	0.515	20.67	0.63
6	LISTA-APT + gradient	0.513	20.46	0.621
7	ResNet-ArtefactCorr + gradient	0.495	19.37	0.568
8	Bas-Protocol + gradient	0.411	17.18	0.459
9	PnP-BM3D (APT) + gradient	0.387	16.56	0.428

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
flight_path_error	-0.07	0.23	mm
voltage_calibration	0.9972	1.0092	-
detection_efficiency	0.586	0.646	-
tip_radius_error	-0.7	2.3	nm

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

Spec DAG — Forward Model Pipeline

S → D

S Sampling

D Detector

Mismatch Parameters

Symbol	Parameter	Description	Nominal	Perturbed
f_p	flight_path_error	Flight path error (mm)	0.0	0.1
v_c	voltage_calibration	Voltage calibration (-)	1.0	1.004
d_e	detection_efficiency	Detection efficiency (-)	0.6	0.62
t_r	tip_radius_error	Tip radius error (nm)	0.0	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.