Center Participants

Joyce McLaughlin
Ford Foundation Professor of Mathematics
Director, IPRPI, Inverse Problems Center at Rensselaer Polytechnic Institute
Rensselaer Polytechnic Institute

Education:
Ph.D., Mathematics, University of California, Riverside, 1968
M.A., Mathematics, University of Maryland, College Park
B.S., Mathematics, Kansas State University

Career Highlights:
McLaughlin is the Ford Foundation Professor in the Department of Mathematical Sciences and the director of IPRPI, the Inverse Problems Center at Rensselaer Polytechnic Institute. She frequently lectures on her work, where applications include medical imaging, ocean acoustics, and inverse problems in vibrating systems. Her distinguished research on inverse problems in vibrating systems was the subject of an invited lecture for the International Congress of Mathematicians in 1994 and for a Conference Board of Mathematical Sciences Lecture Series of eight lectures in 2001. She was awarded the SIAM/AWM Kovalevsky prize and lecture in 2004.

McLaughlin serves on the boards of trustees for the following two organizations: the Institute for Pure and Applied Mathematics (IPAM) at the University of California, Los Angeles from 2002-'05; the Mathematical Sciences Research Institute (MSRI), located at the University of California, Berkeley, from 2003-'06; and on the Scientific Board of the American Institute of Mathematics 2004-. From 1994-'03 she was a member of the Society for Industrial and Applied Mathematics Board of Trustees where she was chair from 1996-'98. Now she is a member of the National Research Council Board of Mathematical Sciences and its Application.

In addition to being an active contributor to her research area, McLaughlin also served as an organizer for special institute semesters on inverse problems at MSRI in 2001, the Statistical and Applied Mathematical Sciences Institute (SAMSI) in 2002, and IPAM in 2003. She also participated in the special institute semesters as a lecturer and long-term participant at MSRI and IPAM. Furthermore, McLaughlin has been a visiting professor at Cornell University, Australian National University, UC Berkeley, and New York University's Courant Institute of Mathematical Sciences.

Since 1998, McLaughlin has been serving on the international advisory board for the journal Inverse Problems. Previously, she was a member of the journal's editorial board from 1992-'97. She is a survey editor, beginning January, 2004, for the European Journal of Applied Mathematics.

Her community service includes spending nine years on the Averill Park Central School District Board of Education.

Research Areas:
Professor McLaughlin's main research area is in nonlinear analysis as it is applied to parameter identification in inverse problems. Her work on the inverse problem of transient elastography and supersonic imaging has the goal of creating images of stiffness properties in biological tissue for use as medical diagnostic tools. She currently leads a National Science Foundation (NSF) Focused Research Group that includes applied mathematicians, engineers, postdoctoral fellows and graduate students. The team's goal is to create images of the variations of shear wave speed in biological tissue. 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. Researchers are developing well-posedness results and fast algorithms for this wave speed recovery. Data measured in a waves and acoustics laboratory at the Ecole Supérieure de Physique et de Chimie Industrielles, Universite Paris VII – as well as synthetic data – are being tested in wave speed recovery algorithms.

A significant breakthrough was established with Dan Renzi and Jeong-Rock Yoon with the development of the arrival time algorithm. This algorithm uses the position of a propagating wave front or the position of a distinguishing feature of the wave as it propagates forward. Initial results with both synthetic and laboratory data are very promising.

McLaughlin's team also investigates inverse problems and wave propagation algorithms in waveguides. In this work, her group develops exact one-way algorithms for calculating the solution of the Helmholtz equation in a range and depth dependent ocean. For inverse problems, the researchers are using their knowledge of waveguides to develop efficient methods for identification of objects and inhomogeneities in waveguides, as well as for time reversal problems where interfaces are identified.

McLaughlin's newest project is the application of time reversal techniques to the identification of fault locations in geophysics. There recorded seismic data from many minor earthquakes are collectively combined, time reversed and used, together with a rough wave speed background map, to sharpen estimates of fault locations.

Furthermore, she studies inverse spectral problems, where the data includes natural frequencies and eigenmode measurements. The inverse problem solution is material parameters such as density, sound speed, or elasticity coefficients. Mathematical models are second or fourth order partial and ordinary differential equations. Well-posedness results are obtained and algorithms are developed and tested. Solution techniques are aimed at maintaining the full nonlinearity of the inverse problem without employing linearization methods. Specific eigenmode measurements that surprisingly yield explicit formulas are the nodal sets of eigenfunctions.

Selected Publication

J. McLaughlin, D. Renzi, K. Parker, C. Wu. "Shear Wave Speed recovery using moving interference patterns obtained in sonoelastography experiments", JASA, Vol. 121 (4), 2007, pp.2438-4226.(text of paper)

J. McLaughlin, Daniel Renzi, Jeong-Rock Yoon. "Anisotropy reconstruction from wave fronts in transversely isotropic acoustic media" SIAM J. Appl. Math Vol. 68, Issue 1, 2007, pp. 24-42. (text of paper)

J. McLaughlin (with Daniel Renzi, Jeong-Rock Yoon, R. L. Ehman, A. Manducca), "Variance Controlled Shear Stiffness Images for MRE Data", IEEE International Symposium on Biomedical Imaging: Macro to Nano, 2006, pp. 960-963. (text of paper)

Joyce McLaughlin (with S. Dediu), "Recovering inhomogeneities in a waveguide using eigensystem decomposition", Inverse Problems, vol.22, June, 2006, pp.1227-1246. (text of paper)

J. McLaughlin (with D.Renzi) "Shear Wave Speed Recovery in Transient Elastography and Supersonic Imaging Using Propagating Fronts", Inverse Problems, 22 , pp. 681-706, (2006). (text of paper of paper with figures).

J. McLaughlin (with D.Renzi) "Using Level Set Based Inversion of Arrival Times To Recover Shear Wavespeed In Transient Elastography And Supersonic Imaging " Inverse Problems, 22 , pp. 707-725, (2006) (text of paper with figures).

L. Ji and J. McLaughlin, "Recovery of the Lamé Parameter µ in Biological Tissues," Inverse Problems, 20, (1), 1-24, (2004). (text of paper with figures)

L. Ji and J. McLaughlin, "Using a Hankel Function Expansion to Identify Stiffness for the Boundary Impulse Input Experiment," AMS Contemporary Mathematics (CONM) Book Series: Proceedings of the Conference on Inverse Problems and Applications, eds. G. Allessandrini and G. Uhlman, Pisa, Italy; (2003). (text of paper with figures)

L. Ji, J. McLaughlin, D. Renzi, and J.-R. Yoon, "Interior Elastodynamics Inverse Problems: Shear Wave Speed Reconstruction in Transient Elastography," Inverse Problems, Special Issue on Imaging, 19, (6), S1-S29, (2003). (text of paper with figures)

B. Geist and J. McLaughlin, "Asymptotic Formulas for the Eigenvalues of the Timoshenko Beam," Journal of Mathematical Analysis and Applications, 253, 341-380, (2001). (text of paper)

J. McLaughlin, "Solving Inverse Problems with Spectral Data," Surveys on Solution Methods for Inverse Problems, eds. D. Colton, H. Engl, A. Louis, J. McLaughlin, and W. Rundell, Springer, New York, 169-194, (2000). (text of paper with figures)

O.H. Hald and J. McLaughlin, "Inverse Problems: Recovery of BV Coefficients from Nodes," Inverse Problems, 14, (2), 245-273, (1998). (text of paper without figures)

S. Wang and J. McLaughlin, "Recovery of a Vertically Stratified Seabed in Shallow Water," in Mathematical and Numerical Aspects of Wave Propagation, ed. J.A. DeSanto, SIAM, Philadelphia, 232-236, (1998). (text of paper with figures)

O.H. Hald and J. McLaughlin, Inverse Nodal Problems: Finding the Potential from Nodal Lines, American Mathematical Society (AMS) Memoir, 119, (572), (1996). (introduction)

Y.Y. Lu and J. McLaughlin, "Propagation in Helmholtz Waveguides using DtN, NtD and R_atD Maps: Part I, a Second Order Method," submitted. (text of paper with figures)

Contact Information:
Joyce McLaughlin
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
110 Eighth Street
Troy, N.Y. 12180 USA
(518) 276-6349
(518) 276-4824 (fax)
mclauj@rpi.edu
http://eaton.math.rpi.edu/faculty/J.McLaughlin/mclauj.html

Francis Sanchez – Assistant
(518) - 276-2145
mclauj3@rpi.edu

Back to top

Inverse Problems Center at Rensselaer
Rensselaer Polytechnic Institute, 110 8th St., Troy, NY 12180-3590.
(518) 276-2145• E-mail: mclauj3@rpi.edu