PET

Positron Emission 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
🥇	U-Net-PET U-Net-PET Ronneberger et al. variant, MICCAI 2020 36.8 dB SSIM 0.977 Checkpoint unavailable	0.852	36.8	0.977	✓ Certified	Ronneberger et al. variant, MICCAI 2020
🥈	PET-ViT PET-ViT Smith et al., ICCV 2024 36.38 dB SSIM 0.975 Checkpoint unavailable	0.844	36.38	0.975	✓ Certified	Smith et al., ICCV 2024
🥉	PETFormer PETFormer Li et al., ECCV 2024 35.7 dB SSIM 0.972 Checkpoint unavailable	0.831	35.7	0.972	✓ Certified	Li et al., ECCV 2024
4	TransEM TransEM Xie et al., 2023 33.7 dB SSIM 0.938 Checkpoint unavailable	0.781	33.7	0.938	✓ Certified	Xie et al., 2023
5	DeepPET DeepPET Haggstrom et al., MIA 2019 32.4 dB SSIM 0.918 Checkpoint unavailable	0.749	32.4	0.918	✓ Certified	Haggstrom et al., MIA 2019
6	OS-EM OS-EM Hudson & Larkin, IEEE TMI 1994 28.92 dB SSIM 0.899 Try in SpecLab →	0.681	28.92	0.899	✓ Certified	Hudson & Larkin, IEEE TMI 1994
7	ML-EM ML-EM Shepp & Vardi, IEEE TPAMI 1982 28.41 dB SSIM 0.889 Try in SpecLab →	0.668	28.41	0.889	✓ Certified	Shepp & Vardi, IEEE TPAMI 1982
8	MAPEM-RDP MAPEM-RDP Nuyts et al., 2002 28.5 dB SSIM 0.815 Try in SpecLab →	0.632	28.5	0.815	✓ Certified	Nuyts et al., 2002
9	FBP-PET FBP-PET Analytical baseline 26.65 dB SSIM 0.849 Try in SpecLab →	0.619	26.65	0.849	✓ Certified	Analytical baseline
10	OSEM OSEM Hudson & Larkin, IEEE TMI 1994 24.8 dB SSIM 0.690 Try in SpecLab →	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
🥇	PET-ViT + gradient PET-ViT + gradient Smith et al., ICCV 2024 Score 0.775 Correct & Reconstruct →	0.775	0.802 34.16 dB / 0.962	0.778 33.2 dB / 0.954	0.744 30.97 dB / 0.930	✓ Certified	Smith et al., ICCV 2024
🥈	U-Net-PET + gradient U-Net-PET + gradient Ronneberger et al. variant, MICCAI 2020 Score 0.753 Correct & Reconstruct →	0.753	0.808 34.45 dB / 0.964	0.735 30.38 dB / 0.922	0.715 28.47 dB / 0.890	✓ Certified	Ronneberger et al. variant, MICCAI 2020
🥉	PETFormer + gradient PETFormer + gradient Li et al., ECCV 2024 Score 0.730 Correct & Reconstruct →	0.730	0.816 34.57 dB / 0.965	0.706 28.1 dB / 0.883	0.667 25.92 dB / 0.830	✓ Certified	Li et al., ECCV 2024
4	OS-EM + gradient OS-EM + gradient Hudson & Larkin, IEEE TMI 1994 Score 0.683 Correct & Reconstruct →	0.683	0.707 27.28 dB / 0.865	0.666 26.03 dB / 0.833	0.676 27.05 dB / 0.859	✓ Certified	Hudson & Larkin, IEEE TMI 1994
5	TransEM + gradient TransEM + gradient Xie et al., 2023 Score 0.678 Correct & Reconstruct →	0.678	0.762 30.99 dB / 0.931	0.679 27.19 dB / 0.863	0.593 22.95 dB / 0.729	✓ Certified	Xie et al., 2023
6	DeepPET + gradient DeepPET + gradient Haggstrom et al., MIA 2019 Score 0.673 Correct & Reconstruct →	0.673	0.741 29.52 dB / 0.909	0.677 26.67 dB / 0.850	0.602 23.47 dB / 0.749	✓ Certified	Haggstrom et al., MIA 2019
7	ML-EM + gradient ML-EM + gradient Shepp & Vardi, IEEE TPAMI 1982 Score 0.634 Correct & Reconstruct →	0.634	0.668 25.8 dB / 0.826	0.651 25.56 dB / 0.819	0.584 23.39 dB / 0.746	✓ Certified	Shepp & Vardi, IEEE TPAMI 1982
8	FBP-PET + gradient FBP-PET + gradient Analytical baseline Score 0.617 Correct & Reconstruct →	0.617	0.635 24.49 dB / 0.785	0.637 25.02 dB / 0.803	0.578 22.61 dB / 0.715	✓ Certified	Analytical baseline
9	MAPEM-RDP + gradient MAPEM-RDP + gradient Nuyts et al., IEEE TMI 2002 Score 0.588 Correct & Reconstruct →	0.588	0.704 27.33 dB / 0.866	0.557 21.52 dB / 0.669	0.504 19.8 dB / 0.589	✓ Certified	Nuyts et al., IEEE TMI 2002
10	OSEM + gradient OSEM + gradient Hudson & Larkin, IEEE TMI 1994 Score 0.566 Correct & Reconstruct →	0.566	0.626 23.79 dB / 0.761	0.556 21.33 dB / 0.661	0.517 20.25 dB / 0.611	✓ 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	0.816	34.57	0.965
2	U-Net-PET + gradient	0.808	34.45	0.964
3	PET-ViT + gradient	0.802	34.16	0.962
4	TransEM + gradient	0.762	30.99	0.931
5	DeepPET + gradient	0.741	29.52	0.909
6	OS-EM + gradient	0.707	27.28	0.865
7	MAPEM-RDP + gradient	0.704	27.33	0.866
8	ML-EM + gradient	0.668	25.8	0.826
9	FBP-PET + gradient	0.635	24.49	0.785
10	OSEM + gradient	0.626	23.79	0.761

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
attenuation	-5.0	10.0	%
scatter_frac	0.25	0.4
timing_res	150.0	300.0	ps
normalization	-2.0	4.0	%

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	PET-ViT + gradient	0.778	33.2	0.954
2	U-Net-PET + gradient	0.735	30.38	0.922
3	PETFormer + gradient	0.706	28.1	0.883
4	TransEM + gradient	0.679	27.19	0.863
5	DeepPET + gradient	0.677	26.67	0.85
6	OS-EM + gradient	0.666	26.03	0.833
7	ML-EM + gradient	0.651	25.56	0.819
8	FBP-PET + gradient	0.637	25.02	0.803
9	MAPEM-RDP + gradient	0.557	21.52	0.669
10	OSEM + gradient	0.556	21.33	0.661

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
attenuation	-6.0	9.0	%
scatter_frac	0.24	0.39
timing_res	140.0	290.0	ps
normalization	-2.4	3.6	%

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	PET-ViT + gradient	0.744	30.97	0.93
2	U-Net-PET + gradient	0.715	28.47	0.89
3	OS-EM + gradient	0.676	27.05	0.859
4	PETFormer + gradient	0.667	25.92	0.83
5	DeepPET + gradient	0.602	23.47	0.749
6	TransEM + gradient	0.593	22.95	0.729
7	ML-EM + gradient	0.584	23.39	0.746
8	FBP-PET + gradient	0.578	22.61	0.715
9	OSEM + gradient	0.517	20.25	0.611
10	MAPEM-RDP + gradient	0.504	19.8	0.589

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
attenuation	-3.5	11.5	%
scatter_frac	0.265	0.415
timing_res	165.0	315.0	ps
normalization	-1.4	4.6	%

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

PET images the 3D distribution of a positron-emitting radiotracer (e.g. 18F-FDG) by detecting coincident 511 keV annihilation photon pairs along lines of response (LORs). The forward model is a system matrix encoding the detection probability for each voxel-LOR pair, incorporating attenuation, scatter, randoms, and detector response. Reconstruction uses iterative ML-EM/OSEM algorithms with attenuation correction from co-registered CT. Low count rates yield Poisson noise; time-of-flight (TOF) information improves SNR.

Principle

Positron Emission Tomography detects pairs of 511 keV gamma rays emitted in opposite directions when a positron from a radiotracer annihilates with an electron. Coincidence detection of the two photons defines a line of response (LOR). Many LORs from different angles are reconstructed into a 3-D activity distribution map, providing functional and metabolic information.

How to Build the System

A PET scanner consists of a ring of scintillation detector blocks (LYSO or LSO crystals coupled to SiPMs) surrounding the patient. Each detector block has a matrix of small crystals (3-4 mm pitch). Coincidence electronics pair detected events within a timing window (4-6 ns for TOF-PET). Modern digital PET systems achieve 200-300 ps timing resolution for time-of-flight. Daily quality checks include detector normalization, timing calibration, and sensitivity phantom scans.

Common Reconstruction Algorithms

OSEM (Ordered Subset Expectation Maximization)
3D OSEM with resolution modeling (PSF reconstruction)
TOF-OSEM (time-of-flight enhanced OSEM)
Attenuation correction from CT (PET/CT) or Dixon MR (PET/MR)
Deep-learning PET denoising (low-count to full-count prediction)

Common Mistakes

Incorrect attenuation correction map (misregistration between PET and CT)
Patient motion between PET and CT causing attenuation-emission mismatch
Metal artifacts in CT propagating into PET attenuation correction
Scatter correction errors in patients with large body habitus
SUV calculation errors from incorrect weight, dose, or timing entries

How to Avoid Mistakes

Verify PET-CT registration quality; use respiratory gating for thorax/abdomen
Minimize time between CT and PET acquisitions; co-register if needed
Use MAR-corrected CT or MR-based attenuation correction to avoid metal artifacts
Use Monte Carlo scatter correction models validated for the patient population
Double-check injected dose, patient weight, injection time, and decay correction

Forward-Model Mismatch Cases

The widefield fallback produces a blurred (64,64) image, but PET acquires sinogram data of shape (n_angles, n_radial) from coincidence detection of annihilation photon pairs — output shape (32,64) vs (64,64)
PET measurement physics (positron emission → annihilation → 511 keV photon pair → coincidence detection) is fundamentally different from optical blur — the fallback cannot model attenuation correction, scatter, randoms, or detector normalization

How to Correct the Mismatch

Use the PET operator that models the system matrix: y = A*x + scatter + randoms, where A encodes line-of-response geometry and attenuation
Reconstruct using OSEM (Ordered Subsets Expectation Maximization) with the correct system matrix, attenuation map, and scatter/randoms estimates

Experimental Setup — Signal Chain

Experimental setup diagram for Positron Emission Tomography

Reconstruction Gallery — 4 Scenes × 3 Scenarios

Method: CPU_baseline | Mismatch: nominal (nominal=True, perturbed=False)

I Ideal II Mismatch (uncorrected) III Oracle correction

I — Ideal

Ground Truth

Measurement

Reconstruction

31.49880178312459 dB SSIM 0.5193170591899157

II — Mismatch

Ground Truth

Measurement

Reconstruction

12.56175850482871 dB SSIM 0.827291096086316

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

22.101099826673153 dB SSIM 0.06966410138598797

I — Ideal

Ground Truth

Measurement

Reconstruction

37.06042713083209 dB SSIM 0.9128698475720882

II — Mismatch

Ground Truth

Measurement

Reconstruction

16.58784940349521 dB SSIM 0.889185955585003

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

31.159360010621164 dB SSIM 0.6124986968298927

I — Ideal

Ground Truth

Measurement

Reconstruction

33.43293807359701 dB SSIM 0.7073451793944836

II — Mismatch

Ground Truth

Measurement

Reconstruction

17.14501391128453 dB SSIM 0.8863799910234061

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

21.17095917446864 dB SSIM 0.11658751399378403

I — Ideal

Ground Truth

Measurement

Reconstruction

29.858000444230118 dB SSIM 0.44687827329704166

II — Mismatch

Ground Truth

Measurement

Reconstruction

12.674989616932601 dB SSIM 0.8182181289773537

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

19.478695397304264 dB SSIM 0.042580221824063444

Mean PSNR Across All Scenes

32.96254185794595 dB

I — Ideal

14.742402859135263 dB

II — Mismatch

23.477528602266805 dB

III — Oracle

Degradation: -18.2 dB Recovery: +8.7 dB

Per-scene PSNR breakdown (4 scenes)

Scene	I (PSNR)	I (SSIM)	II (PSNR)	II (SSIM)	III (PSNR)	III (SSIM)
scene_00	31.49880178312459	0.5193170591899157	12.56175850482871	0.827291096086316	22.101099826673153	0.06966410138598797
scene_01	37.06042713083209	0.9128698475720882	16.58784940349521	0.889185955585003	31.159360010621164	0.6124986968298927
scene_02	33.43293807359701	0.7073451793944836	17.14501391128453	0.8863799910234061	21.17095917446864	0.11658751399378403
scene_03	29.858000444230118	0.44687827329704166	12.674989616932601	0.8182181289773537	19.478695397304264	0.042580221824063444
Mean	32.96254185794595	0.6466025898633823	14.742402859135263	0.8552687929180197	23.477528602266805	0.210332633508432

Experimental Setup

Instrument: Siemens Biograph Vision / GE Discovery MI

Matrix Size: 256x256

Reconstruction: 3D TOF-OSEM

Iterations: 3

Subsets: 17

Post Filter Fwhm Mm: 5.0

Isotope: 18F-FDG

Scan Duration Min: 10

Administered Activity Mbq: 370

Dataset: TCIA, AutoPET Challenge

Key References

Shepp & Vardi, 'Maximum likelihood reconstruction for emission tomography', IEEE TMI 1, 113-122 (1982)
Gatidis et al., 'AutoPET Challenge 2022', MICCAI 2022

Canonical Datasets

AutoPET Challenge (whole-body FDG-PET/CT)
TCIA PET/CT collections

Spec DAG — Forward Model Pipeline

Π(LOR) → Σ_t → D(g, η₃)

Π Line-of-Response Projection (LOR)

Σ Temporal Integration (t)

D Scintillation Detector (g, η₃)

Mismatch Parameters

Symbol	Parameter	Description	Nominal	Perturbed
μ	attenuation	Attenuation map error (%)	0	5.0
f_s	scatter_frac	Scatter fraction error	0.3	0.35
Δt	timing_res	Timing resolution jitter (ps)	200	250
n	normalization	Detector normalization error (%)	0	2.0

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.