Joyce McLaughlin
David Isaacson
Antionette Maniatty
Assad Oberai
Steven Roecker
Birsen Yazici
Mourad Zeghal
Research Scientists
Affiliates 
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,
geophysics
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, was appointed an inaugeral SIAM Fellow in 2009, and an inaugeral AMS Fellow in 2011.
McLaughlin serves on the Scientific Board of the American Institute of
Mathematics (2004present).
In addition she has served 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. From 1994'03 she
was a member of the Society for Industrial and Applied Mathematics (SIAM)
Board
of Trustees where she was Chair from 1996'98; and from 20032007 she was
a member of the National Research Council (NRC) 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
longterm participant at MSRI and IPAM and again at MSRI in 2011. 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 was a survey editor
from 20042012, 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 work on
the inverse problem of transient elastography and supersonic imaging and in magnetic resonance elastography has
the goal of creating images of stiffness properties in biological tissue
for use as medical diagnostic tools. She currently leads a research team
supported by NIH.
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 wellposedness 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, at Mayo Clinic, at Charite Hospital in Berlin and at the
University of Rochester  as well as synthetic data  are being tested
in wave speed
recovery algorithms.
A significant breakthrough was established with Dan Renzi and JeongRock
Yoon with the development of the arrival time algorithm. This algorithm
uses the arrival time of a propagating wave front or the arrival time of a
distinguishing feature of the wave as it propagates forward. Initial
results with both synthetic and laboratory data are very promising.
Newer algorithms with Kui Lin, Ning Zhang and Ashley Thomas are provably stable and image viscoelastic properties of
tissue, over a range of frequencies, from time harmonic displacement data.
McLaughlin's team investigates inverse problems and wave
propagation algorithms in waveguides. In this work, her group develops
exact oneway 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 geophysics project is the application of time reversal
techniques to the identification of fault locations. 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. Wellposedness 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 Publications:
2015
J. McLaughlin, "Overview of Inverse Problems", Encyclopedia of Applied and Computational Mathematics, Vol. 2 LZ, pp. 11191128, 2015.(text of paper)
2014
N. Honda, J. McLaughlin, G. Nakamura, "Conditional Stability for a Single Interior Measurement", Inverse Problems, Vol. 30, No. 5, 2014, 19 pages.(text of paper)
2013
Jessica Jones, "Statistical Comparison of Shear Wave Speed Recovery Using the Direct Algorithm and the Arrival Time Algorithm", A thesis approved by the Graduate Faculty of Rensselaer Polytechnic Institute, May 2013.
2012
Klein, J., McLaughlin, J. and Renzi, D. "Improving Arrival Time Identification in Transient Elastograph", Physics in Medicine and Biology. 57(8), 21 Apr 2012, Pages 21512168. (text of paper)
McLaughlin, J.R., Oberai, A. and Yoon, JR., "Formulas for detecting a spherical stiff inclusion from interior data: A sensitivity analysis for the Helmholtz equation," Inverse Problems, 28 (2012) 084004. (text of paper)
Zheglova, P.; McLaughlin, J. R.; Roecker, S. W.; Yoon, J. R.; Renzi, D.,"Imaging quasivertical geological faults with earthquake data", In: Geophysical Journal International, June, 2012, Vol. 189, Issue 3, pp.15841596 (text of paper)
2011
J. Mclaughlin, JR Yoon. "Arrival times for the wave equation", Communications on Pure and Applied Mathematics (CPAM), Vol. (64)
no. 3, March 2011, pp. 313327. (text of paper)
Lin, K., Mclaughlin, J., Thomas, A., Parker, K., Castaneda, B., and Rubens, D. "Twodimensional shear wave speed and crawling wave speed recoveries from in vitro prostate data". Journal of Acoustical Society of America130(1):58598., July 2011 (text of paper)
Mclaughlin, J., Thomas, A., and Yoon, J.R."Basic Theory for Generalized Linear Solid Viscoelastic Models". AMS Contemporary Mathematics Volume: Tomography and Inverse Transport Theory, editors: G. Bal, D. Finch, P. Kuchment, J. Schotland, P. Stefanov, and G. Uhlmann. 2011, pp. 101134. (text of paper)
S. Ahmed, S. Bak, J. McLaughlin, and D. Renzi. "A Third Order Accurate Fast Marching Method for the Eikonal Equation in Two Dimensions," SIAM J. Scientific Computing 33(5): 24022420 (2011). (text of paper)
2010
S. Bak, J. McLaughlin, and D. Renzi. "Some Improvements for the Fast Sweeping Method," SIAM Journal on Scientific Computation (SISC) (32), 2010, pp. 28532874.(text of paper)
K. Lin, J. McLaughlin, D. Renzi. Thomas, A. "Shear wave speed recovery in sonoelastography using crawling wave data," Journal of the Acoustical Society, July 2010, 128(1):8897. (text of paper)
J. McLaughlin, N. Zhang, and A. Manducca. "Calculating shear modulus and pressure by 2D logelastographic methods", Inverse Problems, Vol. 26, no.8, August 2010, pp. 25. (text of paper)
S. Roecker, J. McLaughlin, B. Baker. "A FiniteDifference Algorithm for Full Waveform Teleseismic Tomography". International Journal of Geophysics, 2010, 181, 1017–1040. (text of paper)
2009
J. McLaughlin and K. Lin. "An error estimate on the direct inversion model in shear stiffness imaging", Inverse Problems, Vol 25(7), July, 2009. (text of paper)
J. McLaughlin, K. Lin, N. Zhang."Logelastographic and nonmarching full inversion schemes for shear modulus recovery from single frequency elastographic data", Inverse Problems, Vol 25(7), July, 2009. (text of paper)
2007
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.24384226.(text of paper)
J. McLaughlin, Daniel Renzi, JeongRock Yoon. "Anisotropy reconstruction from wave fronts in transversely isotropic acoustic media" SIAM J. Appl. Math Vol.
68, Issue 1, 2007, pp. 2442. (text of paper)
2006
J. McLaughlin (with Daniel Renzi, JeongRock 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. 960963. (text of paper)
Joyce McLaughlin (with S. Dediu),
"Recovering inhomogeneities in a waveguide using eigensystem decomposition", Inverse Problems, vol.22,
June, 2006, pp.12271246. (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. 681706, (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. 707725, (2006) (text of
paper with figures).
2004
J. McLaughlin and J.R. Yoon, "Unique
Identifiability of Elastic Parameters from Time Dependent Interior
Displacement Measurement," Inverse Problems, 20,
(1) 2545, (2004). (text
of paper with figures)
L. Ji and J. McLaughlin, "Recovery
of the Lamé Parameter µ in Biological Tissues," Inverse Problems, 20, (1), 124, (2004). (text
of paper with figures)
2003
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), S1S29,
(2003). (text of
paper with figures)
2001
B. Geist and J. McLaughlin, "Asymptotic
Formulas for the Eigenvalues of the Timoshenko Beam," Journal
of Mathematical Analysis and Applications, 253, 341380,
(2001). (text
of paper)
2000 and Prior (selected publications)
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, 169194,
(2000). (text
of paper with figures)
O.H. Hald and J. McLaughlin, "Inverse
Problems: Recovery of BV Coefficients from Nodes," Inverse
Problems, 14, (2), 245273, (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, 232236, (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)
Contact Information:
Joyce McLaughlin
Inverse Problems Center (IPRPI) Director
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
110 Eighth Street
Troy, N.Y. 12180 USA
(518) 2766349
(518) 2764824 (fax)
mclauj@rpi.edu
Jackie Cortese
Administrative Assistant
Inverse Problems Center (IPRPI)
(518)  2762145
mclauj3@rpi.edu
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