Guillaume Bal | Sharpening Images Through Mathematics

Guillaume Bal
Professor of Applied Physics and Applied Mathematics
This profile is included in the publication Excellentia, which features current research of Columbia Engineering faculty members.
Photo by Eileen Barroso

In medical imaging, physicians need high-resolution images with high contrast, so they can see what’s inside the body, down to the submillimeter level. Such images allow physicians to pinpoint treatment, so they can eradicate disease-causing tissue without harming healthy tissue that surrounds it. Researchers use varying techniques to create images of what’s inside the body.

Ultrasound techniques, for example, produce high-resolution images but sometimes with little contrast, so it’s hard to discern healthy from unhealthy tissue. Optical tomography, which uses infrared light, produces images with high contrast but poor resolution. Photoacoustic tomography is a new multi-physics modality for obtaining high-contrast, high-resolution images of human tissues.

Guillaume Bal specializes in the field of mathematical inverse problems, working in the theoretical realm and collaborating with scientists and engineers who are exploring ways to develop new methods for imaging. He has developed mathematical models for several modalities of medical imaging, including optical tomography, photoacoustics, and several other novel multi-physics modalities combining ultrasound with optical or elastic waves.

Photoacoustics is seen as a promising modality for obtaining accurate imaging of tissue in the human brain. His work also helps inform applications in earth science, where researchers work to create images of what exists below the surface of Earth.

Bal also develops mathematical models to analyze equations with random coefficients. He uses such equations for problems involving water or seismic waves moving through geologic formations, sound waves moving through the ocean, or light streaming through the atmosphere. These models look at phenomena at the macroscopic scale, which is more amenable to computations and parameter estimation. Such analyses are crucial in the field of uncertainty quantification with a wide array of applications ranging from dynamics in nuclear waste disposals to uncertainties in climate modeling.

Bal joined Columbia Engineering in 2001 as an assistant professor of applied mathematics. In the fall of 2003, he was a visiting scholar at the Institute for Pure and Applied Mathematics at the University of California-Los Angeles. Bal has also taught at the University of Chicago and was a postdoctoral research associate at Stanford University.

He is the recipient of the 2011 Calderón prize. Other awards include an Alfred P. Sloan Fellowship in 2003 and an NSF Career Award, also in 2003.

Diplôme, École Polytechnique (France), 1993; Ph.D., University of Paris VI (France), 1997

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