# 2d image reconstruction from 1D images

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oneill38 on 24 Nov 2020
Commented: Bjorn Gustavsson on 24 Nov 2020
Hi everyone,
I am facing a problem with image resconstruction and hope you could help me to find a way to do what I am looking for. I will try to make it as clear as possible :
I have a 2D dimensional non uniform (7cm diameter) beam and a 1D detector to image that beam. The detector is a square of 7x7 cm and is composed of 10 vertical strips. The beam is incoming onto the detector perpendicularly and produce a 1D image (10 strips) . Then I rotate the detector by 1° and acquire another image and do this for angles between 0 and 180°. With that set of images I would like to reconstruct the 2D-image of the beam.
I would like to know if there is some premade function to do this. I have looked around the iradon function but I fear this solution does not correspond to my problem since it is made for 1D projection gathered rotating around the object.
From my problem what I need (I think) is a function that superimpose the 1D images all together and normalize the values. I am not really sure whether or not I have to consider my images as 1D images or 2D-like images (10 x 10 times the same value for exemple)...
If anyone as some ideas on how to do this, please fell free to help.

Rik on 24 Nov 2020
I agree with Bjorn: this is how I would sketch the basics for a sinogram and Radon transform.
Image Analyst on 24 Nov 2020
So are you're essentially wanting to do a reconstruction of the entire thing from projections? This is exactly how CT (computed tomography) works. I don't have code for CT reconstruction from projections. It's not easy - after all the guy won a Nobel prize for it.
Bjorn Gustavsson on 24 Nov 2020
@Image Analyst, yeah, but Cormac (as far as I recall) used the central slice theorem to numerically solve/calculate the inverse radon-transform, and we can use iradon - it is great to be spoilt by those who paved the way and dug the ditches...

Bjorn Gustavsson on 24 Nov 2020
Edited: Bjorn Gustavsson on 24 Nov 2020
That definitely looks like the text-book definition of the Radon-iRadon transform pair setup. The limitation here is the 10 strips. That is a rather low number of line-integrals to get, but the geometry is the same.
Perhaps you can extract some additional resolution in the l-direction by making small shifts in the l-direction and deconvolve for sub-strip-with variations - but I guess that's for later. Try with iradon and good luck!
HTH

oneill38 on 24 Nov 2020
Yes. I guess next time I will draw the sketch first before asking ^^'.
About making shifts to virtually increase the resolution ; I can do this experimentally actually. So this is a very good idea and I did not think about it to be honest. Thanks for the tip !
Bjorn Gustavsson on 24 Nov 2020
There's a Swedish cartoon that argues agains that in "the most colourful" language, that I want to but will not quote...
My pleasure. Please update us with the results - because this is something I'm interested in from a fundamental level.