Dokmanic looks to solve molecular imaging puzzle

Picture the following situation: You are visiting relatives, and as you enter the house you clumsily knock over a priceless vase. You try to put the pieces back together, but they all look the same. If only there were labels telling you which ones go together. ECE ILLINOIS Assistant Professor Ivan Dokmanic is attempting to develop such labels, but instead of applying them to a broken vase, he is dealing with distances between points that can't be seen with the naked eye.

His research specifically applies to powder diffraction — a technique used to analyze powdered substances that are too dense to be examined by x-rays.  Powder diffraction can only tell scientists what distances exist in a molecule, but now how they are arranged or which atoms they connect. If scientists could label the atoms, it would allow them to better reconstruct the molecule, solving an age-old mathematical challenge.

“We’re trying to develop new algorithms to find a solution previously found by heuristics,” Dokmanic, assistant professor at the CSL, said. “We want to have theoretical guarantees that our algorithms succeed under given circumstances.”

Dokmanic is one of the few researchers to apply distance geometry to molecular imaging. Previous research either assumes the labels are available or it addresses the problem using brittle approaches that assume perfect, noiseless measurements.

”It turns out that in many real applications, you don’t have the labels,” Dokmanic said. “This class of problems is showing up more and more often, as we find new, more indirect ways to look at the world. Many of the applications are old, but the experimental techniques and ways to approach them are new.”

Dokmanic‘s method also has applications in acoustics and indoor localization, where it models the challenge of associating echoes to walls.

His project, “Combinatorial Inverse Problems in Distance Geometry,” is funded for one year by the National Science Foundation for $157,079. Dokmanic is also affiliated with the CSL.