Public

Atom Probe Tomography (APT) — Public Tier

(5 scenes)

Full-access development tier with all data visible.

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

Load HDF5 → compare reconstruction vs x_true → check consistency → iterate.

Reconstructed signals (x_hat) and corrected spec as HDF5.

✓

True spec visible — use these exact values for Scenario III oracle reconstruction.

Parameter	Spec Range	True Value	Unit
flight_path_error	-0.1 – 0.2	0.05	mm
voltage_calibration	0.996 – 1.008	1.002	-
detection_efficiency	0.58 – 0.64	0.61	-
tip_radius_error	-1.0 – 2.0	0.5	nm

Method: CPU_baseline — Mismatch parameter: nominal

33.04 dB

SSIM 0.8313

21.66 dB

SSIM 0.3376

22.75 dB

SSIM 0.4197

Per-scene breakdown (4 scenes)

Scene	PSNR I	SSIM I	PSNR II	SSIM II	PSNR III	SSIM III
scene_00	32.90	0.8330	21.36	0.3538	22.69	0.4393
scene_01	32.93	0.8361	21.23	0.3703	22.66	0.4596
scene_02	33.03	0.8183	21.98	0.3053	22.85	0.3832
scene_03	33.32	0.8377	22.06	0.3211	22.79	0.3966

#	Method	Score	PSNR	SSIM	Consistency	Trust	Source
1	DiffusionAPT + gradient	0.807	33.75	0.959	0.93	✓ Certified	Inspired by Chung et al., ICLR 2023 (score-based MRI)
2	EquivAPT + gradient	0.799	33.42	0.956	0.91	✓ Certified	Adapted from equivariant vision transformer for atomic imaging, 2025
3	APT-Former + gradient	0.759	30.67	0.926	0.91	✓ Certified	Moody et al., Microsc. Microanal. 30(2):341, 2024
4	TrajectoryPINN + gradient	0.726	28.88	0.898	0.89	✓ Certified	De Geuser & Gault, Annu. Rev. Mater. Res. 52:1, 2022
5	LISTA-APT + gradient	0.694	27.23	0.864	0.88	✓ Certified	Gregor & LeCun, ICML 2010; adapted for APT 2020
6	ResNet-ArtefactCorr + gradient	0.682	26.77	0.852	0.87	✓ Certified	Wei et al., Ultramicroscopy 206:112817, 2019
7	PnP-BM3D (APT) + gradient	0.624	24.1	0.772	0.87	✓ Certified	Danielyan et al., IEEE TIP 21(9):3884, 2012
8	Tikhonov-Trajectory + gradient	0.547	21.02	0.647	0.89	✓ Certified	Geiser et al., Microsc. Microanal. 13(6):437, 2007
9	Bas-Protocol + gradient	0.514	19.67	0.583	0.92	✓ Certified	Bas et al., Appl. Surf. Sci. 87-88:298, 1995

y H_ideal spec_ranges x_true true_spec

Format: HDF5

Scenes: 5

0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖)

PSNR: 40% SSIM: 40% Consistency: 20%