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.<p>> 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
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.
Sounds more like the point is that math research has high ROI compared to most federally funded research
If folks are interested, I recently published a paper [1] demonstrating that fMRI activity in the visual cortex is remarkably high-dimensional!<p>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.<p>[1] <a href="https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1013714" rel="nofollow">https://journals.plos.org/ploscompbiol/article?id=10.1371/jo...</a>
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.<p>[1] <a href="https://fintualist.com/chile/ciencia/los-efectos-de-las-polemicas-de-trump-con-las-universidades-el-caso-de-las-resonancias-magneticas/" rel="nofollow">https://fintualist.com/chile/ciencia/los-efectos-de-las-pole...</a>
[2] <a href="https://mathstodon.xyz/@tao/114956840959338146" rel="nofollow">https://mathstodon.xyz/@tao/114956840959338146</a>
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).<p>[0] q.bio
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.
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.<p>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.
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.
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