CT Reconstruction Simulator: Back-Projection & Hounsfield Units Explained

simulator advanced ~12 min
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HU = −200 — fatty tissue range

A tissue with μ = 0.2 cm⁻¹ at 70 keV yields approximately −200 HU, consistent with fat. Water is defined as 0 HU, air as −1000 HU, and dense bone exceeds +1000 HU.

Formula

HU = 1000 × (μ_tissue − μ_water) / μ_water
Δθ = 180° / N (angular sampling step)
δ ≈ π·D / (2·N) (Nyquist spatial resolution limit)

From Projections to Images

A CT scanner rotates an X-ray source around the patient, recording attenuation profiles at hundreds of angles. Each profile is a line integral of the tissue's linear attenuation coefficient along the beam path. The mathematical challenge — recovering a 2D map from its 1D projections — was solved by Johann Radon in 1917 and implemented in hardware by Godfrey Hounsfield in 1971, earning him the Nobel Prize.

Filtered Back-Projection

Simple back-projection smears each projection back across the image, producing a blurred result. Applying a ramp filter in Fourier space before back-projection corrects for the 1/r blurring, yielding sharp cross-sectional images. This filtered back-projection (FBP) algorithm remains the workhorse of clinical CT, though iterative methods are gaining ground for dose reduction.

Hounsfield Units & Tissue Contrast

The Hounsfield scale normalises attenuation to water (0 HU) and air (−1000 HU). Fat sits near −100 HU, muscle at +40 HU, and cortical bone above +1000 HU. Iodinated contrast agents push vascular HU values to 200-400, enabling angiography. This simulation lets you see how changing μ shifts the HU reading and alters the reconstructed image contrast.

Resolution, Dose & Artifacts

More projections improve resolution but increase radiation dose. Under-sampling creates streak artifacts; metal implants cause beam hardening; patient motion blurs edges. Modern scanners balance these trade-offs with dual-energy acquisition, iterative reconstruction, and sub-second rotation. Adjusting parameters here reveals how each factor shapes the final diagnostic image.

FAQ

What is filtered back-projection in CT?

Filtered back-projection (FBP) is the standard algorithm for reconstructing CT images. Each X-ray projection is filtered to remove blurring, then 'smeared' back across the image plane at the angle it was acquired. Summing many projections recovers the cross-sectional attenuation map of the patient.

What are Hounsfield units?

Hounsfield units (HU) are a linear scale mapping X-ray attenuation coefficients to clinically meaningful numbers. Water is defined as 0 HU, air as −1000 HU, and dense cortical bone typically reads +1000 HU or higher. The scale was introduced by Godfrey Hounsfield, co-inventor of the CT scanner.

How many projections does a clinical CT scanner use?

Modern multi-detector CT scanners acquire between 700 and 1400 projections per 360° rotation, with rotation times under 0.3 seconds. More projections reduce streak artifacts and improve spatial resolution.

What determines spatial resolution in CT?

Spatial resolution depends on the number of projections, detector element size, focal spot size, reconstruction kernel, and slice thickness. Typical clinical resolution is 0.3-0.6 mm in-plane and 0.5-1.0 mm along the z-axis.

Sources

Embed

<iframe src="https://homo-deus.com/lab/biomedical-imaging/ct-reconstruction/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub