Thks a lot for this upload. I am nuclear medicine technologist with no formal training. I was basically a radiographer. These uploads help me a lot. Thks once again
This is not a Wiener filter exactly, but it is indeed similar. The version here with a constant is very similar to Tikhonov regualrisation for least squares problems. A Wiener filter would have a value of c that varies according to the noise level for a given spatial frequency k. Hence would have c(k) instead of just c.
Excellent question. I have other videos which cover this already. But I have not yet covered it in this new series - it will arrive eventually. Short answer: we use a matrix with columns holding all the different PSFs, to do the forward model of the blurred image. Then we can do a least-squares solution to find the true object, which when forward modelled with that matrix, gives the blurred image. Note that we need to store all the different PSFs in a matrix for this approach, and it can be memory intensive.
@@fernando316moncada Thanks for the feedback. Here is the video (old) for a shift-variant PSF: ruclips.net/video/rX0hBXwKeQo/видео.htmlsi=leu_LhuocZt1aHZq
Thanks for the video professor, I've been learning a lot from all your videos. I have a question-perhaps not related to this video. Is there publicly available phantom data I can use to practice image reconstruction? I am particularly interested in emission tomography, so SPECT or PET data would be great. My goal is to implement common algorithms (MLEM, OSEM, FBP) and some of my own ideas, and test them on the phantom data so that I can self-study. A measurement data together with a measurement matrix (system matrix) would be great.
Many thanks for the question - sorry for my delay! Yes, there are many options. One in particular is a phantom that I worked on: zenodo.org/record/8045458 (the Med Phys paper should also cite other brain phantoms). Hope that gives a start, happy to mention other phantoms if you need further advice. Best wishes.
![BLACK BAG - Official Trailer [HD] - Only in Theaters March 14](http://i.ytimg.com/vi/Du0Xp8WX_7I/mqdefault.jpg)
Thks a lot for this upload. I am nuclear medicine technologist with no formal training. I was basically a radiographer. These uploads help me a lot. Thks once again
Many thanks for the feedback, good to know that these videos are helpful!
The image reconstruction series is so thorough and is really helping my intuition. Thanks!
Many thanks for the feedback, appreciated!
The last equation where the c constant is added, is the kernel of the wiener filter, isn't it?
This is not a Wiener filter exactly, but it is indeed similar. The version here with a constant is very similar to Tikhonov regualrisation for least squares problems. A Wiener filter would have a value of c that varies according to the noise level for a given spatial frequency k. Hence would have c(k) instead of just c.
How can we do a deconvolution of a shif-variant PSF?
Excellent question. I have other videos which cover this already. But I have not yet covered it in this new series - it will arrive eventually. Short answer: we use a matrix with columns holding all the different PSFs, to do the forward model of the blurred image. Then we can do a least-squares solution to find the true object, which when forward modelled with that matrix, gives the blurred image. Note that we need to store all the different PSFs in a matrix for this approach, and it can be memory intensive.
@@AndrewJReader Very interesting. Thanks for the answer and thanks for sharing this lectures. 😀
@@fernando316moncada Thanks for the feedback. Here is the video (old) for a shift-variant PSF: ruclips.net/video/rX0hBXwKeQo/видео.htmlsi=leu_LhuocZt1aHZq
Thanks for the video professor, I've been learning a lot from all your videos. I have a question-perhaps not related to this video. Is there publicly available phantom data I can use to practice image reconstruction? I am particularly interested in emission tomography, so SPECT or PET data would be great. My goal is to implement common algorithms (MLEM, OSEM, FBP) and some of my own ideas, and test them on the phantom data so that I can self-study. A measurement data together with a measurement matrix (system matrix) would be great.
Many thanks for the question - sorry for my delay! Yes, there are many options. One in particular is a phantom that I worked on: zenodo.org/record/8045458 (the Med Phys paper should also cite other brain phantoms). Hope that gives a start, happy to mention other phantoms if you need further advice. Best wishes.