Greg Buzzard
Professor of Mathematics
Director of CCAM

Research

Much of my recent work is joint with Charlie Bouman in Purdue ECE. We've developed methods for dynamic sampling and reconstruction with a variety of sensing modalities. At a more fundamental level, we've developed the foundations of the Plug and Play method for image reconstruction into a formulation we call Consensus Equilibrium, which gives a principled framework for reconciling sensing data and external information, such as a preferred denoising method, even when one or both of these information sources is not easily cast in an optimization framework.
 
My previous work encompassed topics in cellular signaling networks and Raman spectroscopy, with earlier work on dynamics in several complex variables. The underlying unifying ideas are methods and algorithms for uncertainty quantification and reduction of uncertainty through appropriate measurement schemes. In conjunction with a number of collaborators, my work in these areas has led to theoretical advances in the construction of surrogate functions and the use of such functions for sensitivity analysis and experiment design, to extensions of the classical theory of optimal design of experiment, and to new algorithms for supervised classification. These theoretical advances have fueled a wide variety of applications, including novel experiment design and control methods for cellular-level control of immune cell response, a Raman spectroscopy system that significantly outperforms previous methods in the high-speed regime, and an adaptive approach for sampling images that forms the basis for algorithms for electron microscopy and other imaging modalities.