# Joyce McLaughlin

## Ford Foundation Professor of Mathematics, IPRPI Director

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.

McLaughlin was first known for her work in inverse spectral theory, in which national frequencies and/or subsets of mode shapes, such as nodal sets, of a vibrating system are used to identify physical properties. She presented this work in 8 Conference Board of Mathematical Sciences Lectures in 2001. Furthermore, her work in this area was presented at the International Congress of Mathematicians in Zurich in 1994,

More recently she has become known for her work in biomechanical imaging of tissue. The physical process that produces the data is the dynamic movement of tissue at a low amplitude of displacement (on the order of microns) and the model for that process is used to create images of biomechanical tissue properties. These images are being utilized, together with ultrasound or MRI images, as a new medical diagnostic tool. The biomechanical imaging work was the subject of McLaughlin’s AWM/SIAM 2004 Kovalevsky Lecture and prize.

McLaughlin also works in shallow water acoustics finding biomasses in ocean waveguides and in geophysics where the goal is to identify fault geometry from frequent low level earthquakes in the fault region.

She is an inaugural Fellow of the Society for Industrial and Applied Mathematics Society (SIAM), an inaugural Fellow of the American Mathematical Society, a member of the Scientific Board of (AIM) American Institute for Mathematics, and a member of the International Advisory Board for the journal Inverse Problems.

### Education

Ph.D., Mathematics, University of California, Riverside, 1968

M.A., Mathematics, University of Maryland, College Park

B.S., Mathematics, Kansas State University

### Selected Publications

- J. McLaughlin, "Overview of Inverse Problems", Encyclopedia of Applied and Computational Mathematics, Vol. 2 L-Z, pp. 1119-1128, 2015.(text of paper)
- Naofumi Honda, Joyce McLaughlin and Gen Nakamura, “Conditional Stability for a Single Interior Measurement” Inverse Problems, 2014, vol. 30, 1-19.
- 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 2151-2168. (text of paper)
- McLaughlin, J.R., Oberai, A. and Yoon, J-R., "Formulas for detecting a spherical stiff inclusion from interior data: A sensitivity analysis for the Helmholtz equation," Inverse Problems, 28 (2012) 084004.
- Zheglova, P.; McLaughlin, J. R.; Roecker, S. W.; Yoon, J. R.; Renzi, D.,"Imaging quasi-vertical geological faults with earthquake data", In: Geophysical Journal International, June, 2012, Vol. 189, Issue 3, pp.1584-1596 (text of paper)
- Mclaughlin, J., J-R Yoon, “Arrival times for the wave equation”, Communications on Pure and Applied Mathematics (CPAM), March 2011, (64) issue 3, pp. 313-327.
- Lin, K., Mclaughlin, J., Thomas, A., Parker, K., Castaneda, B., and Rubens, D. "Two-dimensional shear wave speed and crawling wave speed recoveries from in vitro prostate data". Journal of Acoustical Society of America130(1):585-98., July 2011
- 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. 101-134.
- 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):88-97
- S. Roecker, J. McLaughlin, B. Baker. "A Finite-Difference Algorithm for Full Waveform Teleseismic Tomography". International Journal of Geophysics, 2010, 181, 1017–1040.
- J. McLaughlin, K. Lin, N. Zhang."Log-elastographic and non-marching full inversion schemes for shear modulus recovery from single frequency elastographic data", Inverse Problems, Vol 25(7), July, 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.
- 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.
- 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.
- 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.
- Joyce McLaughlin (with S. Dediu), "Recovering inhomogeneities in a waveguide using eigensystem decomposition", Inverse Problems, vol.22, June, 2006, pp.1227-1246.
- 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).
- 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).
- J. McLaughlin and J.-R. Yoon, "Unique Identifiability of Elastic Parameters from Time Dependent Interior Displacement Measurement," Inverse Problems, 20, (1) 25-45, (2004).
- L. Ji and J. McLaughlin, "Recovery of the Lamé Parameter µ in Biological Tissues," Inverse Problems, 20, (1), 1-24, (2004).
- 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).
- 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).