Filtered BackProjection (Radiologic Technologists : Illustrated guide to FBP)
Ғылым және технология
The Filtered BackProjection (FBP) algorithm is the basis for image reconstruction (converting from the measured data to the image) on modern CT scanners. FBP is a fast and direct method to generate CT images. As the name suggests it is composed of two main steps filtering the data (along the row direction in the detector) and performing the backprojection operation where the data is painted back in the image along the direction which it was measured.
chapters:
00:00 Intro
00:58 CT Image Matrix
02:25 Forward Projection
06:15 Backprojection
08:13 Projection reconstruction
13:48 Sharpening filter
14:43 Filtered Backprojection
15:29 Outro
For more details please see: howradiologyworks.com/FBP
In this video we will go over the details of the projection and backprojection operations first, and then build upon those concepts to discuss the FBP algorithm.
What is Forward Projection in image reconstruction?
The forward projection algorithm is used in iterative reconstruction and gives insight into how projection data is acquired in CT imaging. The forward projection process is an addition operation; where we are adding up values in each pixel along the ray direction as seen in this Figure. This Figure demonstrates parallel beam projections from the left to the right (green arrows) through the image pixels.
In this case you can see that from this single view of parallel beam projections that each of the detector values is the same. So if we have just one view of projection data it will not be
sufficient to reconstruct the image. This is the power of CT imaging compared with x-ray radiography in that more views allows for better differentiation of structures.
In parallel beam acquisitions projection data from 180 degrees is required to be able to accurately reconstruct the object. As an example of another forward projection we demonstrate here a projection which is 90 degrees rotated from the first forward projection.
In this case we can see that now different information is available from this projection. In the first forward projection all of the detector data had the same value, and in this case each detector has a different value. It is these unique measurements from each view which come together to enable us to reconstruct a CT image.
The backprojection operation is essentially trying to undo the forward projection operation. Since the forward projection operation mapped from the image into the detector space the backprojection operation maps from the detector back to the image.
What does the data look like in CT and why is it called a sinogram?
In the demonstration above we talked about the mathematical operation of forward projection through the object. When we turn on our x-ray tube and acquire one view on the detector the x-ray system performs the forward projection for us.
For each view you get one projection which corresponds to one line or one row in the sinogram. In the sinogram the x direction usually is the detector channel direction and the y direction is the view direction.
As in this case the sinogram is typically displayed for one detector row. In this toy example we assume that we just have one detector row in our parallel beam system, so this is all the projection data.
As you look at the sinogram you can see that there are several waves or sinusoids which overlap one another in the sinogram. This is where the name sinogram comes from. In fact for each point in the image space there is a well defined cosine wave that it will trace out.
The next step that we want to discuss is the conversion from the sinogram to the image. That process is what we call image reconstruction.
Why not just use Back Projection for Image Reconstruction?
Now we want to make an image from the sinogram. We know that the sinogram is generated from essentially a forward projection through the object (by the x-rays themselves).
The obvious first step would be to use the backprojection operation to make the image since we know that is doing a reverse type operation to the forward projection. So lets see what happens if we use just backprojection to make an image.
As we showed above the backprojection operation will spread back the information into the image for each view. One analogy you could use is that the backprojection operation is like painting the image information back from each view, one view at a time.
So if we perform the backprojection operation for just one view the image will look like a smeared painting where the artist could only pull the brush across one time. As we discussed above each backprojection provides information for that view, but only for that view. That is why the image looks so blurred with information from just one projection.
The power of computed tomography is that we can combine the information from each of the views in order to reconstruct an image.
Watch the short video a few times to see this information populated.
Пікірлер: 67
One of best channels regarding radiology over the internet im very thankful to find ur channel
@HowRadiologyWorks
3 жыл бұрын
Thanks for the words of support, these comments help me know I’m on the right track.
Again helping the new generation with some key concepts! Thx doc big hugs from Italy ❤️🔥☢️
@HowRadiologyWorks
Жыл бұрын
Thanks for teaching the next generation 😀
Had difficulty understanding the FBP concept but thankfully I came across your video! Helped a lot in visualising how FBP works, thank you!😃
@HowRadiologyWorks
Жыл бұрын
You’re welcome. We have separate videos on the filter and back-projection too if you need more details.
Finally a plain English explanation of FBP. Thanks!
@HowRadiologyWorks
Жыл бұрын
Glad it was helpful Erik☺️
Thank you so much sir and hats off for your dedication and love to provide us with the best 💖
@HowRadiologyWorks
8 ай бұрын
You’re welcome. Thanks for dropping the comment.
God bless you for this explanation
@TheNettforce
3 жыл бұрын
No problem
Best explanation I've found so far. Thanks a lot of bro!
@HowRadiologyWorks
2 жыл бұрын
Thanks, really appreciate it.
@binhnq_tokyo_shorts_24
2 жыл бұрын
@@HowRadiologyWorks Anyway, just have one question. When it comes to 3D reconstruction, are we gonna use the same approach (spreading evenly but in 3D rotation)?
@TheNettforce
2 жыл бұрын
@@binhnq_tokyo_shorts_24 yes we follow the opposite of the path of the x-rays during acquisition. So all pointed from the detector cells to the focal spot. In modern scanners this is a cone shape so it is called cone-beam CT
finally after a year course of radiology i got it, thank you so much
@HowRadiologyWorks
Жыл бұрын
You’re welcome, glad you liked it
Incredibly superb ! What an euro imagination. Gr8 Way of teaching
@TheNettforce
2 жыл бұрын
Thanks Dark Horse, please share with your friends and coworkers
@TheNettforce
2 жыл бұрын
Also check out our channel for other videos especially the one on iterative recon
@kalpeshparlikar
2 жыл бұрын
@@TheNettforce 👍
amazing dude, what a wonderfull concept you have given to me
@HowRadiologyWorks
Жыл бұрын
You’re welcome Harsh
thank you for the concept it was really helpful
@HowRadiologyWorks
8 ай бұрын
Glad to hear that! Thanks for the comments, they are the fuel for me.
Highly valuable content. Thanks from a radiology resident
@HowRadiologyWorks
Жыл бұрын
Glad it was helpful! Thanks Rad Resident. Where about in the world are you?
@kamaltariqbouchakour5533
Жыл бұрын
@@HowRadiologyWorks Hey. I'm located in Algeria
Thanks a bunch, you really made it easy for me to understand the topic :)
@HowRadiologyWorks
Ай бұрын
Glad to hear that! Thanks for the comment
A good video, thanks!
@HowRadiologyWorks
3 жыл бұрын
Thanks jicheng.
That was very understandable. Thanks, and i subscribed
@HowRadiologyWorks
4 күн бұрын
Awesome, thank you! Share the Rad Love with your colleagues
Simple and easy. Great work Dr Brian Question? Is FBP still the main method used in reconstruction today or it it substituded by Iterative reconstruction ?
@HowRadiologyWorks
Жыл бұрын
We have another video on iterative reconstruction which you may have encountered. FBP is typically used as the first guess for iterative CT so it is still important.
@abdovitamins6331
Жыл бұрын
@@HowRadiologyWorks yea u think i have seen it. I will revise the channel. Thanks a lot for your response.
Also my college camp have more than 10k students im spread your channel in the Whatsapp group of the colleges which have many hundreds once i get permission
@HowRadiologyWorks
3 жыл бұрын
Yea please pass along this channel to others at your college
Your explanation is beautiful, thank you. But I have a question, is it required to be FBP after the Back projection?I mean, filtering it once or twice, before and after the Back projection Please answer as soon as possible sir ❤
@HowRadiologyWorks
Жыл бұрын
Ali the Filter is just done once before the backprojection
@AliAli-gg2tr
Жыл бұрын
@@HowRadiologyWorks Thanks 🌹
We back project the image from sinogram or raw data ??
@TheNettforce
Жыл бұрын
The raw data is corrected by what we call calibrations. It is still in the sinogram space, it is filtered along rows and then backprojected
@kalpeshparlikar
Жыл бұрын
@@TheNettforce thanks sir !
My question is how the machine figure out the voxel attenuation coefficient since its just add them all together along the line path or line integral idk I maybe mistaken for the name so how the machine figure out these pixels values
@HowRadiologyWorks
3 жыл бұрын
The FBP algorithm is one way to figure out the attenuation values from the line integrals. Also iterative reconstruction is another method. These methods are called image reconstruction and take many views of line integrals to perform the reconstruction.
@no-de3lg
3 жыл бұрын
@@HowRadiologyWorks so do i need to study calculus to understand how to get these squares value because I cannot conceptually its so hard
@HowRadiologyWorks
3 жыл бұрын
Peator the line integral is just a fancy way of saying add up the voxel values along a line. When we take an X-ray image this part is done automatically. Then we need to find the values for the image voxels. So the FBP converts the data to images
@no-de3lg
3 жыл бұрын
@@HowRadiologyWorks so how many photons or line integral pass per square cm or mm Also what if pixel size is 1mm and within this 1mm there is many or two different attenuation structure like small calcification smaller than micrometer and air what ct number is assigned to it the average but how they gonna count the attenuation cofe I tried to add the voxels values like from above and 45 degree and right but some lines pass between these two different square values Srry if im confusing u im newbie
@HowRadiologyWorks
3 жыл бұрын
Peator a few questions here: 1) depending on the dose there are usually something like 10,000 X-ray photons per detector
How can I donate to support your channel
@HowRadiologyWorks
3 жыл бұрын
Peator please continue to like, comment and share. I don’t have a donate mechanism setup yet.
Hi sir ...you explained the back projection practically...why u don't explained the filter back projection practically ..I need practical explanation of filter back projection sir..thank you.
@HowRadiologyWorks
2 жыл бұрын
Thanks Kandavel, I can work on it. Luckily the backprojection part is the same so I think you are just asking for a more practical description of the filtering process right?
@kandavelg3547
2 жыл бұрын
@@HowRadiologyWorks yes sir ,thank you
you need to improve sound in your videos, you are missing out with the great content, trust me. Not sure if it's your mic or the way the audio quality is reduced or compressed but you need to listen and compare that to other videos, it will get you much more views through increased comfort reduced drop out feeding youtube algorithm what it wants.
@HowRadiologyWorks
Жыл бұрын
Thanks Nauka for the constructive feedback, I will try to improve the audio more over time
Too slow!, awith annoying background music.
@HowRadiologyWorks
4 ай бұрын
Thanks for your feedback.