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

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Bal The investigator and his students study wave and particlepropagation in heterogeneous media and related inverse problems.More precisely, they analyze the refocusing and stabilityproperties of time reversed waves, which can be used innon-destructive testing and wireless communication. They alsoanalyze photon propagation in human tissues to understand how theproperties of these tissues can be imaged from photon intensitymeasurements. Numerical tools and software are developed tosimulate the aforementioned forward and inverse problems. Theinvestigator also develops a course on theoretical and numericalinverse problems. In many applications a good understanding of wave andparticle propagation in complicated media is necessary: seismicwave propagation generated by earthquakes, acoustic wavepropagation to destroy kidney stones (lithotripsy), microwavepropagation in wireless communication, or photon propagation inoptical tomography, a quite powerful imaging technique to detect,for instance, brain tumors and finger arthritis. The investigatordevises theoretical and numerical tools to analyze wave andparticle propagation and to understand how it can be used tosolve practical problems, such as the maximal capacity ofcommunication that can be obtained in a specific environment, orthe minimal size tumor that can be imaged in optical tomography.It is also a primary goal of the investigator to teach cominggenerations of undergraduate and graduate students the noveltechniques that have emerged recently in the applied mathematicalcommunity to address these problems.