Slice 3D object → project (Radon) → filter → back-project. A pedagogical CT reconstruction tool.
Phantom
Acquisition
In-plane pixel grid. Real CT: 512–1024.
More slices → finer Z resolution, slower.
Few angles → streak artifacts.
Gaussian noise on projection data.
Reconstruction
"None" = classic blurry backprojection.
Display
Like clinical viewers. Narrow width = high contrast.
Initializing…
① Source object (3D)i
X · Y · Z
② Reconstruction (3D, FBP)i
X · Y · Z
③ Axial slice f(x,y) at z=z₀i
z = —
④ Sinogram R[f](ρ,θ)i
θ
ρ
— × —
3D Radon — CT Explorer
Demonstrates Computed Tomography (CT) reconstruction. The 3D object is sliced along Z; for each 2D slice the Radon transform produces a sinogram, which is then filtered and back-projected to reconstruct the slice. Stacking the reconstructed slices rebuilds the volume.
The four panels
① Source — ground-truth phantom. ② Reconstruction — FBP output, stacked. ③ Axial slice — f(x,y) at the selected Z. ④ Sinogram — R[f](ρ,θ) for the current slice.
Phantoms
Shepp-Logan (3D) — the canonical CT test phantom (head-like ellipsoids with varying densities). Defrise — stack of disks; classical test for cone-beam artifacts. Hot rods — parallel cylinders of varying diameter; resolution test.
Things to try
• Drop N_θ to ~20 → streak artifacts emerge in panel ②.
• Add noise → speckle propagates through FBP.
• Switch filter to "None" → see the blurry unfiltered backprojection.
• Bump resolution to 256 → much crisper edges (slower).
• Narrow the window width → high-contrast view (like clinical bone/lung windows).
• Toggle Hide artifacts outside object off to see real reconstruction artifacts; on = clean ground-truth-masked view (cosmetic display filter only).
• ← → keys: scrub Z.
Quality notes
FBP uses linear interpolation in both projection and backprojection (much sharper than nearest-neighbor). Real clinical CT additionally uses 512–1024 px reconstruction, fan-beam geometry with rebinning, and often iterative reconstruction (ASIR, MBIR) which is sharper and quieter than FBP for the same dose. Hounsfield units are not a transform — just a fixed linear rescaling of reconstructed attenuation values to a standardized scale (water = 0 HU).