Inverse NUFFT by finufft #264
Replies: 7 comments
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Dear Stefan,
Sorry, no inversion demos just yet. It is more of a research topic,
application-dependent. For now I suggest you apply CG to the normal
equations, possibly using the diagonal sinc-squared weight
preconditioner from
[GLI] The fast sinc transform and image reconstruction from nonuniform
samples in kk-space. L. Greengard, J.-Y. Lee and S. Inati, Commun. Appl.
Math. Comput. Sci (CAMCOS) 1(1) 121-131 (2006).
If this doesn't make sense, try a simpler area-weighting from the MRI
literature.
What is your application?
Best, Alex
…On Mon, Jan 11, 2021 at 1:41 AM Stefan Zhang ***@***.***> wrote:
I am writing for your kind help on the inverse nufft (3d) method in
python. Are there any possible packages for usage directly? As mentioned in
the troubleshooting (
https://finufft.readthedocs.io/en/latest/trouble.html?highlight=invert#mathematical-issues-and-advice)
part, "In the tutorials we will add examples showing how to invert the
NUFFT; ", while I didn't find it. Thanks a lot.
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Also, NFFT has inverse as a direct call. But it is not as fast as we are,
and I don't know if they have py interfaces...
On Mon, Jan 11, 2021 at 1:25 PM Alex Barnett <[email protected]>
wrote:
… Dear Stefan,
Sorry, no inversion demos just yet. It is more of a research topic,
application-dependent. For now I suggest you apply CG to the normal
equations, possibly using the diagonal sinc-squared weight
preconditioner from
[GLI] The fast sinc transform and image reconstruction from nonuniform
samples in kk-space. L. Greengard, J.-Y. Lee and S. Inati, Commun. Appl.
Math. Comput. Sci (CAMCOS) 1(1) 121-131 (2006).
If this doesn't make sense, try a simpler area-weighting from the MRI
literature.
What is your application?
Best, Alex
On Mon, Jan 11, 2021 at 1:41 AM Stefan Zhang ***@***.***>
wrote:
> I am writing for your kind help on the inverse nufft (3d) method in
> python. Are there any possible packages for usage directly? As mentioned in
> the troubleshooting (
> https://finufft.readthedocs.io/en/latest/trouble.html?highlight=invert#mathematical-issues-and-advice)
> part, "In the tutorials we will add examples showing how to invert the
> NUFFT; ", while I didn't find it. Thanks a lot.
>
> —
> You are receiving this because you are subscribed to this thread.
> Reply to this email directly, view it on GitHub
> <#173>, or unsubscribe
> <https://github.com/notifications/unsubscribe-auth/ACNZRSQ5X4JOIQRR24HEEF3SZKMR5ANCNFSM4V5DQZDQ>
> .
>
--
*---------------------------------------------------------------------~^`^~._.~'
|\ Alex H. Barnett Center for Computational Mathematics, Flatiron
Institute
| \ http://users.flatironinstitute.org/~ahb
646-876-5942
--
*---------------------------------------------------------------------~^`^~._.~'
|\ Alex H. Barnett Center for Computational Mathematics, Flatiron
Institute
| \ http://users.flatironinstitute.org/~ahb
646-876-5942
|
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Dear Alex, |
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Ah, that's good. Since your grid has a regular geometry, you can probably
set up a good quadrature rule on it. This means a weight for each node, so
that integrals are well-approximated. With that done, you don't need to
invert. Simply use the 3d1 to approximate the Euler-Fourier formula for the
Fourier coeffs, multiply by the Fourier coeffs of your convolution
function, then use 3d2 to evaluate back at the original nodes. This is much
faster than inverting. Some of my tutorials on the docs site shows examples
of quadrature. Let me know if need help on that.
…On Tue, Jan 12, 2021 at 12:47 AM Stefan Zhang ***@***.***> wrote:
Dear Alex,
Thanks for your reply. My application is rather straightforward. I have a
set of cylindrical 3d grids. I want to do convolution on that, so I need to
do a NUFFT by finufft first, and then an inversion after some
multiplication.
Best, Stefan
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*---------------------------------------------------------------------~^`^~._.~'
|\ Alex H. Barnett Center for Computational Mathematics, Flatiron
Institute
| \ http://users.flatironinstitute.org/~ahb
646-876-5942
|
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Thanks a lot. Now I am trying as you suggested, and the results would be posted here later. |
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see discussion in thread for issue #182. I hope to write a tutorial soon. |
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A few months ago I added an inverse 1d2 tutorial here: |
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I am writing for your kind help on the inverse nufft (3d) method in python. Are there any possible packages for usage directly? As mentioned in the troubleshooting (https://finufft.readthedocs.io/en/latest/trouble.html?highlight=invert#mathematical-issues-and-advice) part, "In the tutorials we will add examples showing how to invert the NUFFT; ", while I didn't find it. Is it possible to provide some more details on that. Thanks a lot.
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