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Let’s talk about backprojection.
Which is an image reconstruction technique for CT.

Backprojection is the process of using the sinogram to try to recreate the original image.
As a recap, let’s go over how to obtain the sinogram before we talk about backprojection.

Remember, we do not know what the original object looks like; but we can obtain the sinogram with our X-ray beams and detectors.
The horizontal axis is distance r, and the vertical axis is projection angle theta.
Each row of the sinogram represents the attenuation profile along the angle theta.
This is called a projection.

Backprojection is essentially the reverse process.
We want to use the sinogram to reconstruct the original image.
But how do we do this?

Let’s look at one projection.
We backproject this onto the image domain like so.
Here’s another example done with a projection along a different angle.

If we do this for each of our projections and add them all up, we get an OK reconstruction of the original image.

Again, backprojection is basically smearing each of our projections, back onto the image domain.

How does the number of projections affect the backprojected image?
We can see that with a small number of projections, the reconstructed image poorly resembles the original.
Increasing the total number of projections results in a closer image to the original.
But even with a high number of projections, we still get a blurry image.

Why is the image still blurry?
Smearing a projection back onto the image adds values to regions that should not have them.
Also, the edges aren’t as pronounced.
Filtered backprojection is a way to reduce blurriness.

In conclusion, backprojection is a way to approximately reconstruct the original image.
The number of projections affect how the backprojected image looks.
To end, here are some more examples showing backprojection.