CAREER: Time Reversal and Inverse Problems in Wave and Particle Propagation

Columbia University, New York NY

Investigators

Abstract

Bal The investigator and his students study wave and particle propagation in heterogeneous media and related inverse problems. More precisely, they analyze the refocusing and stability properties of time reversed waves, which can be used in non-destructive testing and wireless communication. They also analyze photon propagation in human tissues to understand how the properties of these tissues can be imaged from photon intensity measurements. Numerical tools and software are developed to simulate the aforementioned forward and inverse problems. The investigator also develops a course on theoretical and numerical inverse problems. In many applications a good understanding of wave and particle propagation in complicated media is necessary: seismic wave propagation generated by earthquakes, acoustic wave propagation to destroy kidney stones (lithotripsy), microwave propagation in wireless communication, or photon propagation in optical tomography, a quite powerful imaging technique to detect, for instance, brain tumors and finger arthritis. The investigator devises theoretical and numerical tools to analyze wave and particle propagation and to understand how it can be used to solve practical problems, such as the maximal capacity of communication that can be obtained in a specific environment, or the minimal size tumor that can be imaged in optical tomography. It is also a primary goal of the investigator to teach coming generations of undergraduate and graduate students the novel techniques that have emerged recently in the applied mathematical community to address these problems.