X-ray Computed Tomography
X-ray CT reconstructs cross-sectional images from a set of line-integral projections (sinogram) acquired as an X-ray source and detector array rotate around the patient. The forward model is the Radon transform: y = R*x + n where R computes line integrals along each ray. Sparse-view and low-dose protocols reduce radiation but introduce streak artifacts and noise. Reconstruction uses filtered back-projection (FBP) or iterative methods (MBIR, DL post-processing).
Radon Transform
Poisson
fbp
SCINTILLATOR_DETECTOR
Forward-Model Signal Chain
Each primitive represents a physical operation in the measurement process. Arrows show signal flow left to right.
R(θ) → Π(fan) → D(g, η₁)
Benchmark Variants & Leaderboards
CT
X-ray Computed Tomography
R(θ) → Π(fan) → D(g, η₁)
Standard Leaderboard (Top 10)
| # | Method | Score | PSNR (dB) | SSIM | Trust | Source |
|---|---|---|---|---|---|---|
| 🥇 | CT-FM | 0.972 | 44.1 | 0.974 | ✓ Certified | Wang 2026 |
| 🥈 | PINER-CT | 0.962 | 43.6 | 0.970 | ✓ Certified | Sun 2025 |
| 🥉 | CT-MAE | 0.954 | 43.2 | 0.968 | ✓ Certified | Chen 2024 |
| 4 | Score-CT | 0.946 | 42.8 | 0.965 | ✓ Certified | Gao 2024 |
| 5 | DiffusionMBIR | 0.940 | 42.5 | 0.963 | ✓ Certified | Song 2024 |
| 6 | CTformer | 0.914 | 41.2 | 0.954 | ✓ Certified | Wang 2023 |
| 7 | Eformer | 0.896 | 40.3 | 0.948 | ✓ Certified | Wang 2022 |
| 8 | TransCT | 0.884 | 39.8 | 0.942 | ✓ Certified | Xia 2021 |
| 9 | DiffusionCT | 0.869 | 38.2 | 0.965 | ↻ Reproduced | 2305.18727 |
| 10 | DuDoRNet | 0.857 | 38.5 | 0.931 | ✓ Certified | Zhou 2020 |
Showing top 10 of 25 methods. View all →
Mismatch Parameters (4) click to expand
| Name | Symbol | Description | Nominal | Perturbed |
|---|---|---|---|---|
| center_offset | Δc | Center-of-rotation offset (pixels) | 0 | 1.5 |
| angle_error | Δθ | Gantry angle error (deg) | 0 | 0.5 |
| beam_hardening | β | Beam-hardening coefficient | 0 | 0.03 |
| detector_tilt | φ | Detector tilt (deg) | 0 | 0.2 |
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: radon transform — Mismatch modes: center offset, beam hardening, scatter, motion artifact, metal artifact
Noise: poisson — Typical SNR: 25.0–45.0 dB
Requires: flat field, center of rotation, beam hardening correction, detector response, geometric calibration
Modality Deep Dive
Principle
X-ray Computed Tomography reconstructs cross-sectional images from multiple X-ray projection measurements acquired at different angles around the patient. The Beer-Lambert law governs X-ray attenuation: I = I₀ exp(-∫μ(x,y) dl), and the Radon transform relates projections to the attenuation map. Filtered back-projection or iterative algorithms invert the Radon transform to produce volumetric images.
How to Build the System
A clinical CT scanner consists of a rotating gantry with an X-ray tube (80-140 kVp, 50-800 mA) and a curved detector array (64-320 rows of scintillator-photodiode elements) on opposing sides. The gantry rotates at 0.25-0.5 s per revolution. Helical scanning moves the patient table continuously through the gantry. Key calibrations: air scans, detector gain normalization, beam-hardening correction LUTs, and geometric calibration.
Common Reconstruction Algorithms
- Filtered back-projection (FBP) with Ram-Lak or Shepp-Logan filter
- FDK (Feldkamp-Davis-Kress) for cone-beam geometry
- Iterative reconstruction: SART, OS-SIRT
- Model-based iterative reconstruction (MBIR) with statistical noise model
- Deep-learning reconstruction (FBPConvNet, LEARN, WGAN-VGG for low-dose CT)
Common Mistakes
- Ring artifacts from uncorrected detector gain variations
- Beam-hardening artifacts (cupping, streaks near bone/metal) not corrected
- Patient motion during scan causing blurring and streaks
- Insufficient angular sampling producing streak or aliasing artifacts
- Metal artifacts from implants overwhelming reconstruction algorithms
How to Avoid Mistakes
- Perform regular air calibrations and detector flatfield corrections
- Apply polynomial beam-hardening correction or dual-energy decomposition
- Use gating (cardiac/respiratory) or fast rotation to reduce motion artifacts
- Ensure adequate number of projections (≥ π × detector columns for FBP)
- Use metal artifact reduction algorithms (MAR, iterative forward-projection inpainting)
Forward-Model Mismatch Cases
- The widefield fallback produces a blurred (64,64) image, but CT acquires a sinogram of shape (180,64) via the Radon transform (line integrals at multiple angles) — any reconstruction algorithm expecting sinogram input will crash
- The Gaussian blur preserves spatial structure, but the Radon transform converts spatial information into angular projections — the fallback output bears no physical relationship to X-ray transmission measurements
How to Correct the Mismatch
- Use the CT operator implementing the discrete Radon transform: y(theta,s) = integral of f(x,y) along line at angle theta and offset s, producing a (n_angles, n_detectors) sinogram
- Reconstruct using filtered back-projection (FBP) or iterative algorithms (SART, ADMM-TV) that require the correct Radon transform / back-projection pair
Experimental Setup
Siemens SOMATOM Force / GE Revolution CT
512x512
60
1000
736
120
25% of full dose (quarter-dose)
FBP + DL denoising / end-to-end
LoDoPaB-CT, DeepLesion
Signal Chain Diagram
Key References
- Feldkamp et al., 'Practical cone-beam algorithm', J. Opt. Soc. Am. A 1, 612-619 (1984)
- Leuschner et al., 'LoDoPaB-CT, a benchmark dataset for low-dose CT reconstruction', Scientific Data 8, 109 (2021)
Canonical Datasets
- LoDoPaB-CT (Scientific Data 2021)
- DeepLesion (NIH Clinical Center)
- AAPM Low-Dose CT Grand Challenge