3 ms·

High dimensional geometry is transforming the MRI industry (2017) [pdf]

111 points by nill0 5mo ago

Michael666 5mo ago
[dead]
hansvm 5mo ago
You can do a lot better than this if you redefine the problem from directly generating images with certain contrasts to maximizing information gain, even with weak magnets. They've since basically run out of money and are on life support, but Q Bio [0] had that tech working years ago, able to quickly derive many different image types from an entropy-maximizing scan, though they never deployed that in prod IIRC (again, they're broke). [0] q.bio
tug2024 5mo ago
[dead]
jeffreygoesto 5mo ago
I remember one of my diploma students continued with discrete tomography as PhD, topic "Binary Tomography by Iterating Linear Programs" and I found it super interesting to get down the number of shots and at the same time increasing the accuracy a lot.
davidkipstar 5mo ago
It's a nice review but the end reads like a funding pitch. The most important Mathematicians like donoho and Tao in the US seem to currently experience budget cuts and start to address the public.
- mmooss 5mo ago
  It may be a funding pitch, explicitly. It's not a paper - it has no abstract, no citations, works cited, etc.
yummybrainz 5mo ago
If folks are interested, I recently published a paper [1] demonstrating that fMRI activity in the visual cortex is remarkably high-dimensional! Specifically, using a linear approach (like PCA, but slightly fancier), we find that stimulus-related information is present along many, many dimensions of the neural response---much more than previously expected/reported. [1] https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1013714 https://journals.plos.org/ploscompbiol/article?id=10.1371/jo...
- FL33TW00D 5mo ago
  Hasn't fMRI as a whole been called into question? https://www.nature.com/articles/s41593-025-02132-9 https://www.nature.com/articles/s41593-025-02132-9
  - bonsai_spool 5mo ago
    > Hasn't fMRI as a whole been called into question? https://www.nature.com/articles/s41593-025-02132-9 https://www.nature.com/articles/s41593-025-02132-9 I don't immediately see how that paper's assertion (that some areas' fMRI response is influenced by baseline oxygenation and cerebral blood flow) relate to the reliability of an information modeling experiment?
  - yummybrainz 5mo ago
    Yeah, there's a ton of criticism of fMRI as a method, largely because of a lot of results that are statistically unsound (to say the least)! I tend to think of fMRI data as some highly nonlinear transform of whatever neural activity is occurring in a particular region of the brain, at pretty coarse spatial resolution (~1-3 mm) and pretty bad temporal resolution (~5-15 s). Sure, it's no direct measure of neurons firing, but that doesn't mean there isn't information in the signal that we can interpret and maybe use (see [1] for a recent example of reconstructing seen images from brain activity) As a cognitive neuroscientist, I tend to abstract away a ton of the details (neurons, molecules) and focus on more general computational principles: how do we get complex behavior from many simple interacting units---voxels in fMRI, for instance? Regarding the specific paper you posted, I saw some of the discourse around it but haven't read it carefully myself (it's not my area of expertise). I saw some recent re-analysis of that data [2] that argues that the result isn't valid, but need to look at it more carefully. [1]: https://www.nature.com/articles/s41598-025-89242-3 https://www.nature.com/articles/s41598-025-89242-3 [2]: https://www.biorxiv.org/content/10.64898/2026.04.21.719913v1 https://www.biorxiv.org/content/10.64898/2026.04.21.719913v1
throwaway34018 5mo ago
Having worked through Geometric Tomography by Gardner, one of the big names in the field, I am pretty confident in asserting that the folks in the field have little to no interest in tomography or other applications. It's merely a grant winning ruse. The same field rebrands as "high dimensional probability/stats" by casting the uniform measure on convex bodies in the language of log-concave densities, but you talk to the folks themselves and they smirk about the extent to which they care about whether their work has any relation to the applications they claim. There are some notable exceptions -- Donoho, Vershynin -- but most of them are doing good old fashioned Brunn-Minkowski theory, which is fundamental but a hard sell in its most truthful form.
- jey 5mo ago
  I'm not convinced this is a problem. For example, all the folks who developed convex analysis for its pure geometric and mathematical beauty in the land of pure Platonic forms, well their work was still useful downstream for all of us doing convex optimization and dealing with log-concave probability distributions. So no harm, no foul.
- srean 5mo ago
  > by casting the uniform measure on convex bodies in the language of log-concave densities Can you tell more ? I find the idea very intriguing. I don't know of the connection between the two.
Vexs 5mo ago
It's worth reading this one to the end- the point of this paper isn't about the math involved, it's that this math was the result of the federal funding of maths research. > The cost-benefit ratio of Mathematical research has been off-scale. The Federal government spends about $250 Million/year on mathematics research. Yet in the US there are 40 Million MRI scans per year, incurring tens of billions in Medicaid, Medicare and other Federal costs. The financial benefits of the roughly 10-to-1 productivity improvements now being seen in MRI could soon far exceed the annual NSF budget for mathematics research
- rtkwe 5mo ago
  It's the thing people don't get when they see odd studies being funded and try to judge if they're worthy of being funded. Either it's just they don't understand where the study fits into a larger problem or simply that esoteric studies sometimes leads to surprising findings that are far more useful than anyone could reasonable predict.
  - finghin 5mo ago
    It’s probably more
  - dooglius 5mo ago
    It would be instructive to actually look at the studies in question and whether or not they were odd or esoteric.
- CGMthrowaway 5mo ago
  Sounds more like the point is that math research has high ROI compared to most federally funded research
  - WorkerBee28474 5mo ago
    As the Soviets knew, apparatus are expensive but pencils are cheap.
- lostlogin 5mo ago
fcortes 5mo ago
A couple of months ago I wrote a small post [1] (in Spanish) about subsampled MRI image reconstruction using compressed sensing and how it relates to government funding issues. At the time Tao had written some posts [2] about how the IPAM, where Terrence Tao was working, was losing some funding because UCLA wouldn't follow some new federal government policies. [1] https://fintualist.com/chile/ciencia/los-efectos-de-las-polemicas-de-trump-con-las-universidades-el-caso-de-las-resonancias-magneticas/ https://fintualist.com/chile/ciencia/los-efectos-de-las-pole... [2] https://mathstodon.xyz/@tao/114956840959338146 https://mathstodon.xyz/@tao/114956840959338146
danielvaughn 5mo ago
Given that this was published nearly a decade ago, I'd be very interested to see what the SOTA is today.
- olsondv 5mo ago
  Between this and blipped-CAIPI in 2011, there hasn’t been much change from an acquisition perspective in the industry. Mostly everyone shifted to AI reconstruction, workflow improvements, and reducing helium use. Those are the low-hanging fruit. I’d be happy to be proven wrong but I don’t see any major breakthroughs coming from advanced math in the near future. ISMRM was this week though so maybe something came out of it.
blindriver 5mo ago
Our universe is multi-dimensional and we are only 3 dimensional. The only way to understand more about our universe is to try to understand multi-dimensions.
auggierose 5mo ago
That must be the thing that Terence Tao advertises in every podcast I watch with him in it.
bofadeez 5mo ago
quick scroll and saw no math in the paper

111 points by nill0 5mo ago

[dead]

You can do a lot better than this if you redefine the problem from directly generating images with certain contrasts to maximizing information gain, even with weak magnets. They've since basically run out of money and are on life support, but Q Bio [0] had that tech working years ago, able to quickly derive many different image types from an entropy-maximizing scan, though they never deployed that in prod IIRC (again, they're broke). [0] q.bio

tug2024 5mo ago

[dead]

jeffreygoesto 5mo ago

I remember one of my diploma students continued with discrete tomography as PhD, topic "Binary Tomography by Iterating Linear Programs" and I found it super interesting to get down the number of shots and at the same time increasing the accuracy a lot.

davidkipstar 5mo ago

It's a nice review but the end reads like a funding pitch. The most important Mathematicians like donoho and Tao in the US seem to currently experience budget cuts and start to address the public.

mmooss 5mo ago
It may be a funding pitch, explicitly. It's not a paper - it has no abstract, no citations, works cited, etc.

yummybrainz 5mo ago

If folks are interested, I recently published a paper [1] demonstrating that fMRI activity in the visual cortex is remarkably high-dimensional! Specifically, using a linear approach (like PCA, but slightly fancier), we find that stimulus-related information is present along many, many dimensions of the neural response---much more than previously expected/reported. [1] https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1013714 https://journals.plos.org/ploscompbiol/article?id=10.1371/jo...

FL33TW00D 5mo ago
Hasn't fMRI as a whole been called into question? https://www.nature.com/articles/s41593-025-02132-9 https://www.nature.com/articles/s41593-025-02132-9
- bonsai_spool 5mo ago
  > Hasn't fMRI as a whole been called into question? https://www.nature.com/articles/s41593-025-02132-9 https://www.nature.com/articles/s41593-025-02132-9 I don't immediately see how that paper's assertion (that some areas' fMRI response is influenced by baseline oxygenation and cerebral blood flow) relate to the reliability of an information modeling experiment?
- yummybrainz 5mo ago
  Yeah, there's a ton of criticism of fMRI as a method, largely because of a lot of results that are statistically unsound (to say the least)! I tend to think of fMRI data as some highly nonlinear transform of whatever neural activity is occurring in a particular region of the brain, at pretty coarse spatial resolution (~1-3 mm) and pretty bad temporal resolution (~5-15 s). Sure, it's no direct measure of neurons firing, but that doesn't mean there isn't information in the signal that we can interpret and maybe use (see [1] for a recent example of reconstructing seen images from brain activity) As a cognitive neuroscientist, I tend to abstract away a ton of the details (neurons, molecules) and focus on more general computational principles: how do we get complex behavior from many simple interacting units---voxels in fMRI, for instance? Regarding the specific paper you posted, I saw some of the discourse around it but haven't read it carefully myself (it's not my area of expertise). I saw some recent re-analysis of that data [2] that argues that the result isn't valid, but need to look at it more carefully. [1]: https://www.nature.com/articles/s41598-025-89242-3 https://www.nature.com/articles/s41598-025-89242-3 [2]: https://www.biorxiv.org/content/10.64898/2026.04.21.719913v1 https://www.biorxiv.org/content/10.64898/2026.04.21.719913v1

throwaway34018 5mo ago

Having worked through Geometric Tomography by Gardner, one of the big names in the field, I am pretty confident in asserting that the folks in the field have little to no interest in tomography or other applications. It's merely a grant winning ruse. The same field rebrands as "high dimensional probability/stats" by casting the uniform measure on convex bodies in the language of log-concave densities, but you talk to the folks themselves and they smirk about the extent to which they care about whether their work has any relation to the applications they claim. There are some notable exceptions -- Donoho, Vershynin -- but most of them are doing good old fashioned Brunn-Minkowski theory, which is fundamental but a hard sell in its most truthful form.

jey 5mo ago
I'm not convinced this is a problem. For example, all the folks who developed convex analysis for its pure geometric and mathematical beauty in the land of pure Platonic forms, well their work was still useful downstream for all of us doing convex optimization and dealing with log-concave probability distributions. So no harm, no foul.
srean 5mo ago
> by casting the uniform measure on convex bodies in the language of log-concave densities Can you tell more ? I find the idea very intriguing. I don't know of the connection between the two.

Vexs 5mo ago

It's worth reading this one to the end- the point of this paper isn't about the math involved, it's that this math was the result of the federal funding of maths research. > The cost-benefit ratio of Mathematical research has been off-scale. The Federal government spends about $250 Million/year on mathematics research. Yet in the US there are 40 Million MRI scans per year, incurring tens of billions in Medicaid, Medicare and other Federal costs. The financial benefits of the roughly 10-to-1 productivity improvements now being seen in MRI could soon far exceed the annual NSF budget for mathematics research

rtkwe 5mo ago
It's the thing people don't get when they see odd studies being funded and try to judge if they're worthy of being funded. Either it's just they don't understand where the study fits into a larger problem or simply that esoteric studies sometimes leads to surprising findings that are far more useful than anyone could reasonable predict.
- finghin 5mo ago
  It’s probably more
- dooglius 5mo ago
  It would be instructive to actually look at the studies in question and whether or not they were odd or esoteric.
CGMthrowaway 5mo ago
Sounds more like the point is that math research has high ROI compared to most federally funded research
- WorkerBee28474 5mo ago
  As the Soviets knew, apparatus are expensive but pencils are cheap.
lostlogin 5mo ago

fcortes 5mo ago

A couple of months ago I wrote a small post [1] (in Spanish) about subsampled MRI image reconstruction using compressed sensing and how it relates to government funding issues. At the time Tao had written some posts [2] about how the IPAM, where Terrence Tao was working, was losing some funding because UCLA wouldn't follow some new federal government policies. [1] https://fintualist.com/chile/ciencia/los-efectos-de-las-polemicas-de-trump-con-las-universidades-el-caso-de-las-resonancias-magneticas/ https://fintualist.com/chile/ciencia/los-efectos-de-las-pole... [2] https://mathstodon.xyz/@tao/114956840959338146 https://mathstodon.xyz/@tao/114956840959338146

danielvaughn 5mo ago

Given that this was published nearly a decade ago, I'd be very interested to see what the SOTA is today.

olsondv 5mo ago
Between this and blipped-CAIPI in 2011, there hasn’t been much change from an acquisition perspective in the industry. Mostly everyone shifted to AI reconstruction, workflow improvements, and reducing helium use. Those are the low-hanging fruit. I’d be happy to be proven wrong but I don’t see any major breakthroughs coming from advanced math in the near future. ISMRM was this week though so maybe something came out of it.

blindriver 5mo ago

Our universe is multi-dimensional and we are only 3 dimensional. The only way to understand more about our universe is to try to understand multi-dimensions.

auggierose 5mo ago

That must be the thing that Terence Tao advertises in every podcast I watch with him in it.

bofadeez 5mo ago

quick scroll and saw no math in the paper