# Homework Help: How does backprojection of CT scanners cause star blur

1. Aug 25, 2012

### amylase

1. The problem statement, all variables and given/known data

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

Why / how does backprojection cause star blur?

2. Relevant 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

3. 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.

Last edited: Aug 25, 2012