How does backprojection of CT scanners cause star blur

[amylase]

Homework Statement

In the context of image reconstruction using backprojection by CT scanners -

Why / how does backprojection cause star blur?

Homework Equations

Figure 13 of
http://depts.washington.edu/nucmed/IRL/pet_intro/intro_src/section4.html

and

Figure 25-16 of
http://www.dspguide.com/ch25/5.htm

and

Figure (c) of
http://en.wikibooks.org/wiki/Basic_.../X-Ray_CT_in_Nuclear_Medicine#Back_Projection

This link gives a concise explanation of backprojection but still doesn't answer my question about why the spokes.
http://www.medcyclopaedia.com/library/topics/volume_i/b/backprojection.aspx

The Attempt at a Solution

I understand backprojection works by reverse Fourier Transforming projected data from frequency domain back to spatial domain. In otherwords signals from different projections (from different axes) are summed together to give the value the voxel. I'm ok with that.

What I don't understand is, when you add up all the stripes/smears (as shown in the links provided above) which represent each backprojection, you get a polygon. More stripes added up, where ALL stripes overlap just becomes a more sided polygon. I am okay with this also, but why the spokes? That's my question.

The diagrams seem to suggest those spokes / spiky / pointing bits are result of overlapping of adjacent stripes (ie. just adjacent stripes overlapping, not the total summation of all stripes like the middle polygon bit). But we only calculate areas where ALL stripes overlap don't we? so why would those grey spikes (of overlapping of some stripes) come into equation?

Hope my question is clear: why do we get spokes when not even all the stripes overlap at the spokes (and so shouldn't come into equation of our calculation, so why show up in the result?)?

(I'm okay with the polygon bit, but not okay with the spokes)

Thank you.

 

[mark726]

Thank you for your question about backprojection and star blur. The spokes that you see in the backprojection images are a result of the mathematical process of backprojection. When we perform backprojection, we are essentially adding up all the projections from different angles to create a 2D image. However, this process can cause blurring or smearing in the final image.

This blurring or smearing is caused by the fact that not all projections have the same level of information. Some projections may have more information about a particular area of the image, while others may have less. When we add up all these projections, the areas with more information will contribute more to the final image, resulting in a higher intensity. This is why you see the spokes in the backprojection image - they represent the areas where there is a higher concentration of information from the projections.

Additionally, the spokes can also be caused by the fact that backprojection is an approximation method. It is not a perfect reconstruction of the original image, and therefore, there will always be some degree of error or distortion in the final image. This error can manifest as the spokes that you see in the backprojection image.

I hope this helps to answer your question. If you have any further inquiries, please do not hesitate to ask. Keep exploring and learning about backprojection and its applications.