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
SIAM Board of Trustees Chair, 1996-1998
CBMS Lecturer, 2001
Kovalevsky Prize and Lecture, 2004
Fellow of the Society for Industrial and Applied Mathematics, 2009
Professor McLaughlin’s main research area is in nonlinear analysis as applied to parameter identification in inverse problems. Her research includes biomedical, geophysical and ocean wave guide imaging.
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 wave speed in biological tissue; the aim is to develop a medical diagnostic tool. The research includes: (1) fundamental mathematical properties of wave fronts, viscoelastic models and uniqueness and sensitivity results for biomechanical imaging; and (2) algorithms for utilizing in vivo and laboratory data and the creation of biomechanical images. The biomechanical 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.
In addition basic problems in imaging vertical faults in the mantle with passive data have been addressed.
P. Zheglova, J.R. McLaughlin, S.W. Roecker, J.R. Yoon, D. Renzi, “Imaging quasi vertical geologic faults with earthquake data,” accepted (proofs received and returned 2012), Geophys. J. Int. (text of paper)
J.R. McLaughlin, A. Oberai and J-R. Yoon, “Formulas for detecting a spherical stiff inclusion from interior data: A sensitivity analysis for the Helmholtz equation,” accepted, Inverse Problems, special July 2012 issue on coupled physics. (text of paper)
Klein, J., McLaughlin, J. and Renzi, D. “Improving Arrival Time Identification in Transient Elastography”, Physics in Medicine and Biology. 57(8), 21 Apr 2012, Pages 2151-2168. (text of paper)
J. Mclaughlin, J-R Yoon. "Arrival times for the wave equation”, Communications on Pure and Applied Mathematics (CPAM), Vol. (64) no. 3, March 2011, pp. 313-327. (text of paper)
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 (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. 101-134. (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): 2402-2420 (2011). (text of paper)
S. Bak, J. McLaughlin, and D. Renzi. "Some Improvements for the Fast Sweeping Method," SIAM Journal on Scientific Computation (SISC) (32), 2010, pp. 2853-2874.(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):88-97. (text of paper)
J. McLaughlin, N. Zhang, and A. Manducca. "Calculating shear modulus and pressure by 2D log-elastographic methods", Inverse Problems, Vol. 26, no.8, August 2010, pp. 25. (text of paper)
S. Roecker, J. McLaughlin, B. Baker. "A Finite-Difference Algorithm for Full Waveform Teleseismic Tomography". International Journal of Geophysics, 2010, 181, 10171040. (text of paper)
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."Log-elastographic and non-marching full inversion schemes for shear modulus recovery from single frequency elastographic data", Inverse Problems, Vol 25(7), July, 2009. (text of paper)
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. (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).
J. McLaughlin and J.-R. Yoon, "Unique Identifiability of Elastic Parameters from Time Dependent Interior Displacement Measurement," Inverse Problems, 20, (1) 25-45, (2004). (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)
(Additional publications on link below.)