Information gradients and information-based domain partitions of Morse fields

Abstract

The acquisition of spatial data from one or more sensors is of interest in many applications. In ocean monitoring, measurements frequently include ocean temperature, salinity, and CO2 concentration.  Similarly, in medical imaging, there is growing interest in the use of digital infrared thermal imaging (DITI) as an adjunct to mammography and ultrasound for increased reliability in the detection of breast cancer. The talk describes a new approach to quantifying the information content of such measurements of continuously varying scalar fields.  The work is based on recently established connections between differential topology and information theory that provide a theoretical framework for search strategies aimed at rapid discovery of topological features (locations of critical points and critical level sets) of a priori unknown differentiable random fields. The proposed approach to rapid discovery of topological features leads in a natural way to the creation of parsimonious reconnaissance routines that do not rely on any prior knowledge of the environment.  The talk will also discuss a closely related novel approach to data fusion that is aimed at enhancing human perceptual capabilities by extracting and synthetically recombining information-rich measurements from different sensors. 

Biography

John Baillieul's research deals with robotics, the control of mechanical systems, and mathematical system theory. His PhD dissertation, completed at Harvard University under the direction of R.W. Brockett in 1975, was an early work dealing with connections between optimal control theory and what came to be called “sub-Riemannian geometry.” After publishing a number of papers developing geometric methods for nonlinear optimal control problems, he turned his attention to problems in the control of nonlinear systems modeled by homogeneous polynomial differential equations. Such systems describe, for example, the controlled dynamics of a rigid body. His main controllability theorem applied the concept of finiteness embodied in the Hilbert basis theorem to develop a controllability condition that could be verified by checking the rank of an explicit finite dimensional operator. Baillieul’s current research is aimed at understanding decision making and novel ways to communicate in mixed teams of humans and intelligent automata. John Baillieul is a Fellow of IFAC, a Fellow of the IEEE and a Fellow of SIAM.

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