A Primer on Sparse-View CT Reconstruction

CT works by measuring X-ray attenuation from many angles around an object. Collecting fewer views — sparse-view CT — reduces radiation dose and acquisition time, but it breaks the assumptions of the classical reconstruction algorithm.

From projections to sinograms

For an object with density $f(x, y)$, each detector reading is a line integral along the ray $L$:

$$g(\rho, \theta) = \int_L f(x, y)\, dl$$

Stacking the projections for every angle $\theta$ gives the sinogram. A single point inside the object traces a sinusoid across it — hence the name.

Filtered back-projection

FBP applies a ramp filter $|\omega|$ in the frequency domain before smearing each projection back across the image. The central slice theorem guarantees this works — if every angle is sampled.

Where learning helps

The simplest approach lets FBP do the geometry and trains a network to remove artefacts in the image domain:

import torch.nn.functional as F

def training_step(model, sinogram, target, fbp):
    coarse = fbp(sinogram)          # physics: analytical reconstruction
    refined = model(coarse)         # learning: artefact removal
    return F.mse_loss(refined, target)

Physics-guided methods go further by keeping the forward model in the loop, so the network cannot drift away from what the measurements actually say.