MacArthur fellow Emmanuel Candès uses little bits of data to see the big picture
In the world of consumer electronics, a camera that can pack more pixels into a single image is something to boast about. But Emmanuel Jean Candès won a MacArthur Foundation “genius” grant for doing the opposite.
The applied mathematician and statistician from Stanford works in a field called compressed sensing. His discoveries are paving the way for cheaper and more effective medical sensors by following the adage “less is more.”
The award stunned Candès, who received the call in September.
“I was really surprised,” he said. The thrill of the news, he said, still hasn’t worn off.
MacArthur fellows receive a $625,000 grant over five years that they can spend however they see fit. Winners are allowed to tell one person ahead of the announcement, and so the mathematician immediately broke the news to his wife, Chiara Sabatti, a statistical geneticist at Stanford University.
“She thought I was joking,” he said with a laugh.
Compressed sensing involves designing clever algorithms that can use a tiny amount of data to reconstruct an image in impressive detail.
Consider this problem: Digital cameras take pictures by capturing images made of millions of pixels. Then these images are compressed by a program that throws away the redundant pixels and keeps only the important bits.
Candès and other scientists wondered: Why go to the effort of gathering all those pixels if you’re just going to throw them away? Why not just record only the important bits of data in the first place?
For digital cameras, taking in a ton of data isn’t a big problem. After all, silicon is still cheap.
But for devices that rely on wavelengths of light beyond the visible spectrum — say, for the radio waves used in magnetic resonance imaging machines — creating a sensor that could take a good image with less data could make a world of difference.
That’s actually how the problem first arose, Candès said.
Researchers at the University of Wisconsin came to him with a problem. MRI machines typically take several minutes to construct an image of a limb or an organ. During that time, patients have to stay as still as possible. If there was a way to get the same image in less time, it would be a major improvement for both patients and doctors.
Candès developed an algorithm that could reliably create a detailed image with very few data points. His solution depended on a key idea: Most images are not “complex,” per se.
In this context, a complex image would be the static snow on a television set with no signal; there’s no pattern, so it’s hard to predict how the entire image looks based on a few pieces of it.
But something like a Mickey Mouse cartoon is far less complex because it’s full of predictable patterns. This makes it easier for his algorithm to spot things such as edges and colors. That way, instead of encoding every individual red pixel in Mickey’s trousers or black pixel in his ears, the algorithm picks up the outlines of the body, the color of each section and other significant features.
When Candès tested his solution on MRI data, it reconstructed the test image perfectly. He tried a second and a third MRI, and it performed perfectly again.
“I couldn’t believe what he was doing,” said UCLA mathematician Terence Tao, who heard about the work a few years back when he and Candès were dropping their kids off at a child-care center. “It sounded like he was getting a free lunch. It sounded mathematically impossible.”
Tao, a co-recipient of the 2006 Fields Medal, one of the highest honors for mathematicians, said he went home and tried to come up with a mathematical argument showing why Candès’ explanation could not be true. He couldn’t find one, and concluded that the researchers must be right.
He ultimately helped Candès work out a theory to explain why the method was so successful — one that broadened its appeal well beyond MRIs. This principle could be used for a variety of sensing applications, including in medicine, seismology and astronomy.
“He has this knack of taking a real-world practical problem that people actually care about and turning it almost into a math puzzle,” Tao said.
Candès credited many scientists whose work he built on, as well as his graduate students and his scientist wife.
“You always stand on the shoulders of giants,” he said.
In recent years, Candès has switched to another puzzle: the problems with reproducibility in science.
Scientists used to formulate a hypothesis and then gather data to see whether they could prove it wrong, the mathematician said. But now, researchers typically reverse those two steps, and current statistical practices aren’t built to handle the switch.
Many findings may be difficult to reproduce because the math they rely upon isn’t able to pinpoint truly meaningful relationships within large data sets, Candès said.
“The way we conduct science has changed a lot,” he said. “There is a community of statisticians that feel we need to rewrite statistical theory so that it is adapted to this big data world, where we collect data first and then we ask questions later.”
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