Radon Transform / CT Scanner
Watch how a CT scanner reconstructs internal structure. X-ray beams sweep around a phantom object at many angles, each projection recorded as a column in a sinogram. Filtered back-projection then inverts these projections to recover the hidden image. Drag the angle slider to watch the reconstruction sharpen with more data.
Computed tomography (CT) scans the body with X-ray beams from many angles. Each beam measures the total density along its path — a line integral of the attenuation coefficient. This is exactly the Radon transform of the 2D cross-section.
The sinogram collects all these 1D projections: each column is a single angle's projection, and each row corresponds to a detector position. Named for the sinusoidal paths traced by point features as the angle sweeps around.
To reconstruct the image, we use filtered back-projection. Each projection is first convolved with a ramp filter (which sharpens edges and suppresses the blur inherent in naive back-projection), then "smeared" back across the image at the appropriate angle. The contributions from all angles sum to approximate the original density map.
With few angles, the reconstruction is blurry and shows streak artifacts. As you add more angles, the image sharpens. Clinical CT scanners typically use hundreds to thousands of projections. The mathematical foundation was laid by Johann Radon in 1917, but practical CT scanning was developed by Godfrey Hounsfield and Allan Cormack in the 1970s, earning them the 1979 Nobel Prize in Medicine.