Learn CT by doing
An interactive course on the principles of X-ray CT. Starting from attenuation and line integrals, it works through sinograms, backprojection, FBP, cone-beam and industrial CT, iterative reconstruction, dose and image quality, Monte Carlo photon transport, artifacts, and deep learning. The later parts show how the same reconstruction mathematics reappears in MRI and nuclear medicine (PET/SPECT), reach beyond CT to tomosynthesis, photoacoustic, and electron tomography, and cover the image processing of reconstructed images: display, denoising, segmentation, registration, and quantification.
- Math and simulations side by side
- Computes entirely in your browser (Web Worker + WebGPU)
- Available in Japanese and English
It is written for students, radiologic technologists, and engineers who want to understand tomographic imaging both through the mathematics and through intuition. Basic calculus and trigonometry are all that is assumed; every concept is introduced as it appears.
Each chapter opens with a short explanation and the key formulas, followed by an interactive simulation. Don't just read: drag the sliders, press the buttons, and see for yourself how each parameter shapes the projections and the reconstructed image. Reading in order from Chapter 1 is recommended, but feel free to jump to whatever interests you.
Chapters
X-ray CT
CT principles and reconstruction, medical to industrial
Chapter 1X-rays and Attenuation
Move a single ray around to grasp the Beer–Lambert law and what a projection means.
Chapter 2Forward Projection and the Sinogram
See through the Radon transform how an object maps into measured data (the sinogram).
Chapter 3Simple Backprojection
Find out why merely smearing the measurements back produces a 1/r blur.
Chapter 4Filtered Backprojection
Derive the ramp filter from the Fourier slice theorem and arrive at FBP, the standard method.
Chapter 5Fan-Beam & Helical CT
Fan-beam geometry and reconstruction, plus helical scanning and pitch in clinical CT.
Chapter 6Cone-Beam CT and FDK
Run the 3D FDK reconstruction in your browser and observe cone artifacts.
Chapter 7Industrial CT
Rotate the part and magnify it. Geometric magnification and focal-spot size set the resolution for NDT and metrology.
Chapter 8Iterative Reconstruction
ART, SIRT, and MLEM/OSEM: solving the equations iteratively, and low-dose CT.
Chapter 9Dose & Image Quality
Where noise comes from: measuring σ∝1/√dose, CTDI and DLP, and quantitative filter comparison via MTF and NPS.
Chapter 10Monte Carlo Photon Transport
Following photons one at a time through the three interactions. The origin of scatter and dose, and production simulation with Geant4.
Chapter 11Sparse-View Reconstruction
Can the image survive 1/8 of the projections? Compressed sensing and TV regularization (ASD-POCS) compared live.
Chapter 12Artifacts and Their Reduction
Beam hardening, metal, rings, motion, and scatter: see each cause and its remedy in simulation.
Chapter 13Deep Learning and AI for CT
Train a tiny CNN denoiser in your browser and probe the limits of its generalization.
Chapter 14Spectral CT & Photon Counting
Energy is information: live dual-energy material decomposition and VMI, plus a survey of PCCT and the reconstruction research frontier (diffusion models, INRs).
Chapter 15Playground
A laboratory for combining the ingredients of all chapters and comparing two pipelines A/B.
MRI
Magnetic resonance imaging
Chapter 16Magnetization & Relaxation
The MRI part begins: tip the magnetization with RF pulses and watch T1/T2 relaxation and the FID live.
Chapter 17Spatial Encoding & k-Space
Gradients turn position into frequency. Watch an image emerge as k-space fills line by line.
Chapter 18Pulse Sequences & Contrast
Spin-echo refocusing, and designing T1/T2/FLAIR contrast by turning the TR and TE knobs.
Chapter 19Fast Imaging & Compressed Sensing
Undersampling k-space speeds imaging but breaks the image. Compare aliasing vs incoherent artifacts and TV-based CS-MRI.
Nuclear Medicine
Emission tomography (PET/SPECT)
Chapter 20PET/SPECT & Emission Tomography
The nuclear-medicine part: measure radiation emitted from within. Attenuation-corrected MLEM and TOF, where Chapter 8's iterative reconstruction becomes the correct statistical model.
Chapter 21SPECT and the Physics of Collimation
Nuclear medicine. How single photons get a direction. The resolution–sensitivity trade-off of the parallel-hole collimator, via the system-resolution formula and a simulation.
Frontiers
Limited angle, and tomography beyond CT
Chapter 22Tomosynthesis
When you cannot rotate all the way around: depth blur from a limited angular range, and in-plane vs through-plane resolution.
Chapter 23Photoacoustic Tomography
Heat with light, listen with sound: reconstruct internal acoustic sources from detectors on an arc (circular Radon transform).
Chapter 24Electron Tomography
The specimen tilts only ±70°: the missing wedge in Fourier space and the elongation artifact it causes.
Chapter 25Phase-Contrast CT
Frontiers. Measuring the phase of the refractive index, not absorption. Synchrotron propagation-based phase contrast and Paganin retrieval recover the low contrast of soft tissue.
Image Processing
Viewing, cleaning up, and measuring reconstructed images
Chapter 26Image Display and Enhancement
The image-processing part begins. Windowing (WL/WW), histogram equalization, gamma, and MPR/MIP: the first step in viewing a reconstructed image.
Chapter 27Geometric Transforms and Interpolation
The interpolation needed for every rotation, zoom, and warp. Nearest, bilinear, and bicubic, and aliasing.
Chapter 283D Visualization
Isosurface extraction and surface rendering with marching cubes, and volume rendering with transfer functions. Seeing volume data as a solid.
Chapter 29Filtering and Denoising
Linear (Gaussian) and edge-preserving (median, bilateral, non-local means, anisotropic diffusion, TV) denoising. The trade-off between noise and detail.
Chapter 30Frequency-Domain Filtering
Weighting by frequency through the 2D Fourier transform. Low-pass, high-pass, and notch. Removing periodic noise.
Chapter 31Edge Detection and Gradients
Capturing abrupt intensity changes with gradients (Sobel) and the Laplacian. Canny, with non-maximum suppression and hysteresis.
Chapter 32Segmentation
Extracting structures with thresholding (Otsu), region growing, morphology, and connected components. From classical methods to learned (U-Net).
Chapter 33Registration
Rigid, affine, and deformable alignment, similarity metrics (SSD, NCC, mutual information), and multimodal fusion for PET/CT and MR/CT.
Chapter 34Quantification and Radiomics
First-order statistics of ROIs/VOIs, texture (GLCM), shape features, and radiomics. Turning images into numbers. The close of the textbook.