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Algorithms can also learn without examples

In donut-shaped buildings, particle accelerators take super-detailed X-ray images. Yet those images are not good enough to learn how to drive on hydrogen for example. Mathematics PhD student Allard Hendriksen has developed an algorithm that improves the images without having to learn from data from previous measurements, as there is no such data. Promotion 3 March.

Most impressive to Allard Hendriksen were the synchrotrons he visited in Switzerland and France.  'I was familiar with the CT scans with X-rays from the hospital, but these are enormous donuts in the landscape; the one near Grenoble has a diameter of eight hundred meters. Electrons are spinning around in it at about light speed. Wherever they fly out of one of the forty corners, they shoot X-rays out of the ring.'

From driving on hydrogen...

While a CT scan in the hospital sometimes requires you to lie still for minutes, a synchrotron makes ten full 3D reconstructions per second. It is a billion times stronger than the hospital scan. That's not enough to properly track a working fuel cell, for example. 'Toyota wants to make hydrogen driving possible. For that you need to be able to see exactly what is happening in such a fuel cell while it is working. We want as many as three thousand pictures per second.'

...To visualizing every cell of a mouse brain. 

Sometimes the current power is enough, but the object to be examined cannot handle the radiation. 'A piece of brain tissue swells up into a kind of pudding at so much radiation. For example, researchers are working on a complete image of a mouse brain, with all the billions of nerve cells and all the connections between them. This takes years, because now it can only be done by putting microscopically thin slices under the microscope, one by one. A gigantic project that creates a lot of data.'

Allard Hendriksen

Algorithms usually learn from existing datasets

Hendriksen is fond of such large datasets. He developed a self-learning or deep learning algorithm that can show images at the required detail with less radiation or with more speed. Normally, algorithms learn from existing datasets. Feed them lots of brain scans and they understand what brains look like at the level needed to distinguish, say, a tumor. Those data for hydrogen fuel cells and brains at the cellular level is exactly what we don't have.

This algorithm learns from how not to do it

The solution Hendriksen worked out sounds a bit strange. 'I let the algorithm learn from how not to do it. I split the data set in two. With one half set, the algorithm must try to come up with the other set. From one set to the other and vice versa; we can always check how well it fits.'

It really works, and mathematically it's correct

Once the algorithm fills in the gaps well enough, you can trust it to correctly construct a twice as sharp or even sharper image based on the full data set from the scanner. By thinking mathematically about what his algorithm needed to do, Hendriksen was also able to theoretically reason that it could. His results are now being applied to research on brains at the cellular level.

Breakthrough: 299,924 instead of 300 photos per second

All sorts of data researchers gave Hendriksen datasets with which they had already tried everything. 'The best moment was when I was working on a dataset from a fuel cell. It just wouldn't work. Until I started digging into the data. I had been told that the rotation speed was three hundred pictures per second. That turned out to be 299,924. That was the breakthrough, now I understood that the different slices of the 3D image just didn't fit together and kept rotating slightly. After correction, the image suddenly appeared.'


Allard Hendriksen did his PhD research at CWI (the national research institute for mathematics and computer science in the Netherlands) and LIACS (Leiden Institute of Advanced Computer Science). The defense of the thesis will take place on 3 March , 2022. The supervisor is Joost Batenburg. Look here for practical information about the defence.

Text: Rianne Lindhout
Photo: ESRF, Grenoble

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