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, artifacts, and deep learning. The later parts show how the same reconstruction mathematics reappears in MRI and nuclear medicine (PET/SPECT), and reach beyond CT to tomosynthesis, photoacoustic, and electron tomography.
- 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 10Sparse-View Reconstruction
Can the image survive 1/8 of the projections? Compressed sensing and TV regularization (ASD-POCS) compared live.
Chapter 11Artifacts and Their Reduction
Beam hardening, metal, rings, motion, and scatter: see each cause and its remedy in simulation.
Chapter 12Deep Learning and AI for CT
Train a tiny CNN denoiser in your browser and probe the limits of its generalization.
Chapter 13Spectral 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 14Playground
A laboratory for combining the ingredients of all chapters and comparing two pipelines A/B.
MRI
Magnetic resonance imaging
Chapter 15Magnetization & Relaxation
The MRI part begins: tip the magnetization with RF pulses and watch T1/T2 relaxation and the FID live.
Chapter 16Spatial Encoding & k-Space
Gradients turn position into frequency. Watch an image emerge as k-space fills line by line.
Chapter 17Pulse Sequences & Contrast
Spin-echo refocusing, and designing T1/T2/FLAIR contrast by turning the TR and TE knobs.
Chapter 18Fast 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)
Frontiers
Limited angle, and tomography beyond CT
Chapter 20Tomosynthesis
When you cannot rotate all the way around: depth blur from a limited angular range, and in-plane vs through-plane resolution.
Chapter 21Photoacoustic Tomography
Heat with light, listen with sound: reconstruct internal acoustic sources from detectors on an arc (circular Radon transform).
Chapter 22Electron Tomography
The specimen tilts only ±70°: the missing wedge in Fourier space and the elongation artifact it causes.