The 2017 MacArthur “Genius” Fellows were awarded this week. One fellow of particular interest to this blog is mathematician and statistician Emmanuel Candès. The Stanford University professor uses complex mathematical structures to improve the health care system. As stated on the MacArthur website:
Using an approach that draws on concepts from linear algebra and L1 minimization (a concept of high-dimensional geometry), Candès and colleagues were able to reconstruct high-resolution signals from sparse measurements under specified conditions. In diagnostic healthcare, for example, reducing the number of measurements needed to create high-resolution MRI scans shortens the amount of time patients must remain still in the scanner, an outcome with particularly beneficial implications for children. The ability to process and/or reconstruct audio, visual, and wireless signals from limited data has also led to significant refinements in digital photography, radar imaging, and wireless communications.
But how does Candes technique work? A Wired article explains how compressing sensing works.
Compressed sensing works something like this: You’ve got a picture — of a kidney, of the president, doesn’t matter. The picture is made of 1 million pixels. In traditional imaging, that’s a million measurements you have to make. In compressed sensing, you measure only a small fraction — say, 100,000 pixels randomly selected from various parts of the image. From that starting point there is a gigantic, effectively infinite number of ways the remaining 900,000 pixels could be filled in.
The key to finding the single correct representation is a notion called sparsity, a mathematical way of describing an image’s complexity, or lack thereof. A picture made up of a few simple, understandable elements — like solid blocks of color or wiggly lines — is sparse; a screenful of random, chaotic dots is not. It turns out that out of all the bazillion possible reconstructions, the simplest, or sparsest, image is almost always the right one or very close to it.
Very exciting insights that we all hope can greatly improve health care for today’s and tomorrow’s patients.