Ford Foundation Professor of Mathematical Sciences; Member, Faculty of Information Technology; Director, IPRPI
Ph.D. University of California, Riverside
Recent Career Highlights:
ICM Invited Lecture 1994
Professor McLaughlin’s main research area is in nonlinear analysis as applied to parameter identification in inverse problems. In addition, recent new work gives results of numerical algorithms for solving Helmholtz equation.
Several sets of inverse problems are being considered. One of these is the inverse problem of elastography. There the goal is to create images of the variations of shear wavespeed in biological tissue; the aim is to develop a medical diagnostic tool. These images extend the doctor's palpation exam where the doctor presses against the skin to feel the presence of abnormal tissue which is stiffer than normal tissue.A second set of problems are inverse problems and wave propagation algorithms in waveguides. There we develop exact one way algorithms for calculating the solution of Helmholtz equation in a range and depth dependent ocean. For inverse problems we utilize our knowledge of waveguides to develop efficient methods for identification of objects in waveguides and for time reversal problems.
“Recovery of the Lamè parameter µ in biological tissues”, (with Lin Ji), Inverse Problems, Vol. 20, No. 1, February 2004, pp. 1-24.
“Unique identifiability of elastic parameters from time-dependent interior displacement measurement”, (with Jeong-Rock Yoon), Inverse Problems, Vol. 20, No. 1, 2004, pp. 25-46.
“Shear Wave Speed Recovery in Transient Elastography And Supersonic Imaging Using Propagating Fronts”, (with Daniel Renzi), Inverse Problems, Vol. 22, 2006, pp. 681-706.
“Using Level Set Based Inversion of Arrival Times To Recover Shear Wavespeed In Transient Elastography And Supersonic Imaging”, (with Daniel Renzi), Inverse Problems, Vol. 22, 2006, pp. 707-725.
"Anisotrophy Reconstruction From Wave Fronts In Transversely Isotropic Acoustic Media," accepted. SIAMJ. Appl. Math. (Text of Paper [with figures])
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