Image Reconstruction: PET data, backprojection, sinograms, list-mode, convolution

[@learn2444]

Simple,clear and highly intuitive. Thanks for this contribution

[@AndrewJReader]

Many thanks for the feedback!

[@aljamela-is8tb]

amazing brief description of the convolution

[@AndrewJReader]

Thanks for the feedback!

[@AndrewChicco]

Thank you for this well thought out & delivered series of lectures (as all of your lectures are). Could you perhaps consider adding in the (i of j) to the title of each, as it would assist in watching them in sequence.

[@AndrewJReader]

Many thanks for your feedback. In the first instance, perhaps this playlist could help: kzbin.info/aero/PL557uxcMh3xx4XdfAf7eoO94f6AEr8Qun

[@AndrewJReader]

More up to date playlist: kzbin.info/aero/PL557uxcMh3xy_lmu7kgfKM_nY31MDc8UM

[@anshuchoudhary5454]

hello professor this video is extremely useful. I request you to kindly make one video on Fourier Rebinning Algorithm. I am facing some difficulty in understanding and implementing that. With your clear explanation, it could really help me a ton.

[@AndrewJReader]

Hi, thanks for the feedback, really appreciated. For info, the latest version of the video is here: kzbin.info/www/bejne/bn23mmOXqt6taM0 For Fourier rebinning, I did indeed write my own version many years ago, but I do not use it anymore, either doing fully 3D or 2D only. Sorry to say that I will not plan to cover that topic at the moment. I guess you plan to do FORE+FBP?

[@anshuchoudhary5454]

@@AndrewJReader Oh alright professor. I was validating a research article using GEANT4 simulations where they used FORE +FBP for converting 3D sinogram to 2D and then getting the image. What method do you use to get resolution of PET scanner. Is it directly calculable from 3D sinograms.

[@engels_diary]

Great presentation!!

[@AndrewJReader]

Many thanks Charel!

[@morhafhaidar4949]

Thank you for the Video. I have a question: how can i apply that to cone beam ct. what is the training data and the ground truth in this case?

[@AndrewJReader]

Thanks for the comment. In this video there is no machine learning, so no training data or ground truth labels needed. Cone beam CT would have a different ray geometry, and you would need a CT reconstruction method, so all a bit different from this video. You could look up deep learning methods for CT image reconstruction which might more closely match what you need.

[@deepaphysics]

Hello Professor Andrew I am beginner in image reconstruction and was trying to obtain sinogram from the LOR data I got from simulations. I know the underlying concept but putting it into code is becoming difficult for me. I have the coordinates of coincident points. How can I generate sinogram using that ? I am facing difficulty in making a matrix where we can assign value of intensity for a given point. Kindly help me in this regard, I will be really grateful.

[@AndrewJReader]

Hi, thanks for your message. I suggest you take a look at the newer version of this video - towards the end of the video I do give equations at the 36 minutes mark. Here is the link: kzbin.info/www/bejne/bn23mmOXqt6taM0si=BoGpmDftQAm3RYMF Hope that helps, let me know

[@deepaphysics]

@@AndrewJReader Thank you for your reply professor. I understand the equation, will try to embed it. But kindly tell me that when plotting sinogram do we use simple matplotlib function ? How should I plot to get appropriate inverse radon transformation?

[@Dalat_Instruments]

Hello, How to calculate S and phi angle? 5:00

[@AndrewJReader]

Hi, you need to use equations based on the 2 detection coordinates of an event. So, something like phi = arctan ( difference in y positions / difference in x positions). Then s would be something like s = - x sin phi + y cos phi. Hope that helps?

[@Dalat_Instruments]

@@AndrewJReader I mean determine phi and S based on different detector pairs, from which to construct sinogram.

[@AndrewJReader]

@@Dalat_Instruments Yes, that's also what I meant. You need to know the coordinates for each detector, (x1,y1), (x2,y2), that make up a detector pair. Given the coordinates of the 2 detectors, that allows the line joining the 2 detectors to be found (i.e. calculating s and phi).

[@Dalat_Instruments]

@@AndrewJReader detectors are arranged in a circle, why are the coordinates (x,y)?

[@AndrewJReader]

@@Dalat_Instruments Hi, using (x,y) coordinates is more general for various scanners (I used to work with rotating planar detector PET systems). You can of course use a different coordinate system, but if you do, then the way of calculating phi and s will differ. I gave equations above for the general case of specifying (x,y) coordinates. To find s and phi just involves solving a geometric problem in the coordinate system that you choose.