How many Projections do we need in CT?

In this article:
  • CT Image Quality Depends on Projection Count: The number of projections in a CT scan directly affects image clarity, with too few causing star artifacts and noise, while more projections improve contrast-to-noise ratio (CNR).
  • Nyquist-Based Rule for Projection Estimation: A geometric derivation based on the Nyquist theorem suggests that the number of projections should match the number of detector pixels the sample sweeps over during rotation.
  • Blurring Factors Reduce Required Projections: Practical factors like detector resolution, cone-beam geometry, and X-ray focal spot size introduce blur, effectively lowering the number of projections needed for quality imaging.
  • Trade-Off Between Scan Time and Image Quality: While more projections yield better results, users often balance scan duration and dose with acceptable image quality for their specific application.
  • Optimizing CT for Efficiency and Accuracy: Understanding projection requirements helps operators fine-tune CT parameters, ensuring efficient, high-quality non-destructive testing across industries.
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The number of projections in CT

The image quality in a CT volume depends on the number m of projections. How many projections do we really need to avoid under sampling which would cause star artifacts and a noisy appearance? The more the better? 

The rule is often applied to determine m from the number N of pixels the X-ray shadow of the sample swept over during the scan. Why is this the case? Is it really necessary? 

A simple derivation of the rule

This rule can be derived from the famous Nyquist theorem. We use a simple geometric consideration to visualize the background. 

Suppose the X-ray shadow of the scan sweep over N pixels during the scan inscribed to a radius R, then a reconstructed slice is N x N voxels in size as shown in the drawing. It is plausible that the X-ray shadow feature in the scan should not move more than one pixel from one projection to the next. The small angle ∂ is the rotation between the projections.

That means the small arc s should be smaller than one pixel width P. Some geometry and algebra lead to the known rule. Are you missing a factor of 2? Remember that the X-rays go through the sample and count twice.

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Really so many?

If the sample covers, e.g.: a 4000 x 4000 pixel detector, the number of projection is as high as 6300. Many users believe this is not necessary and they are right. Any blurring makes the pixels virtually larger and thus reduces the effective number of pixels. So, we can simply insert another N into the formula.

There are several factors that contribute to that blur: the basic spatial resolution of the detector, the tilted impact of X-rays in cone-beam CT, and the geometric unsharpness induced by the focal spot size. These are known and can be considered when estimating m.

It is often much simpler: the users feel that they see enough and do not want to spend more time. 

Using more projections has an effect similar to a higher exposure time or higher X-ray dose per frame: the Contrast-to-Noise Ratio (CNR) improves. A low number of projections causes a worse CNR and star artefact pattern.