Positron Emission Tomography
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.
System Matrix Emission
Poisson
mlem
SCINTILLATION_DETECTOR
Forward-Model Signal Chain
Each primitive represents a physical operation in the measurement process. Arrows show signal flow left to right.
Π(LOR) → Σ_t → D(g, η₃)
Benchmark Variants & Leaderboards
PET
Positron Emission Tomography
Π(LOR) → Σ_t → D(g, η₃)
Standard Leaderboard (Top 10)
| # | Method | Score | PSNR (dB) | SSIM | Trust | Source |
|---|---|---|---|---|---|---|
| 🥇 | U-Net-PET | 0.852 | 36.8 | 0.977 | ✓ Certified | Ronneberger et al. variant, MICCAI 2020 |
| 🥈 | PET-ViT | 0.844 | 36.38 | 0.975 | ✓ Certified | Smith et al., ICCV 2024 |
| 🥉 | PETFormer | 0.831 | 35.7 | 0.972 | ✓ Certified | Li et al., ECCV 2024 |
| 4 | TransEM | 0.781 | 33.7 | 0.938 | ✓ Certified | Xie et al., 2023 |
| 5 | DeepPET | 0.749 | 32.4 | 0.918 | ✓ Certified | Haggstrom et al., MIA 2019 |
| 6 | OS-EM | 0.681 | 28.92 | 0.899 | ✓ Certified | Hudson & Larkin, IEEE TMI 1994 |
| 7 | ML-EM | 0.668 | 28.41 | 0.889 | ✓ Certified | Shepp & Vardi, IEEE TPAMI 1982 |
| 8 | MAPEM-RDP | 0.632 | 28.5 | 0.815 | ✓ Certified | Nuyts et al., 2002 |
| 9 | FBP-PET | 0.619 | 26.65 | 0.849 | ✓ Certified | Analytical baseline |
| 10 | OSEM | 0.508 | 24.8 | 0.690 | ✓ Certified | Hudson & Larkin, IEEE TMI 1994 |
Mismatch Parameters (4) click to expand
| Name | Symbol | Description | Nominal | Perturbed |
|---|---|---|---|---|
| attenuation | μ | Attenuation map error (%) | 0 | 5.0 |
| scatter_frac | f_s | Scatter fraction error | 0.3 | 0.35 |
| timing_res | Δt | Timing resolution jitter (ps) | 200 | 250 |
| normalization | n | Detector normalization error (%) | 0 | 2.0 |
Reconstruction Triad Diagnostics
The three diagnostic gates (G1, G2, G3) characterize how reconstruction quality degrades under different error sources. Each bar shows the relative attribution.
Model: system matrix emission — Mismatch modes: attenuation correction error, scatter residual, patient motion, randoms subtraction error
Noise: poisson — Typical SNR: 8.0–25.0 dB
Requires: normalization sinogram, attenuation map, scatter correction, dead time correction, decay correction
Modality Deep Dive
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
Siemens Biograph Vision / GE Discovery MI
256x256
3D TOF-OSEM
3
17
5.0
18F-FDG
10
370
TCIA, AutoPET Challenge
Signal Chain Diagram
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