Math 221, Linear Algebra
I grew up in Butte and have gotten most of my education in Montana. After graduating with my Ph.D. in Mathematics from Montana State University in 2002, I did a one-year post-doc at the Statistical and Applied Mathematical Sciences Institute in North Carolina, and then began my current position at the University of Montana (UM) in 2003. While at UM, I have held long-term visiting professorships at the University of Helsinki in Finland, the University of Otago in New Zealand, the Danish Technical University in Denmark, and Monash University in Australia. I became a full professor at UM in 2013. I am married with two grown children.
B.S. Mathematics, Montana Technological University, 1996
M.S. Mathematics, Montana State Univesity, 1998
M.S. Mathematics, University of Oregon, 1999
Ph.D. Mathematics, Montana State University, 2002
Inverse Problems, Uncertainty Quantification, Computational Mathematics, Computational Statistics
Computational Uncertainty Quantification for Inverse Problems, Society for Industrial and Applied Mathematics, 2018. MATLAB codes HERE.
REFEREED PUBLICATIONS: (email me if you'd like a PDF copy of any of these)
56. "Optimization-Based MCMC Methods for Nonlinear Hierarchical Statistical Inverse Problems," with T. Cui, SIAM/ASA J. Uncertainty Quantification, Vol. 9, No. 1, pp. 29–64, 2021.
55. "Semivariogram methods for modeling Whittle-Matérn priors in Bayesian inverse problems," with R. Brown and T. Cui, Inverse Problems, Vol. 36, No. 5, 2020, 055006.
54. "Scalable optimization-based sampling on function space," with T. Cui, Y. Marzouk, Z. Wang, SIAM Journal on Scientific Computing, Vol. 42, No. 2, pp. A1317--A1347, 2020.
53. "MCMC Algorithms for Computational UQ of Nonnegativity Constrained Linear Inverse Problems," with P. C. Hansen, SIAM Journal on Scientific Computing, Vol. 42, No. 2, 2020, pp. A1269--A1288.
52. "Efficient Marginalization-based MCMC Methods for Hierarchical Bayesian Inverse Problems," with A. Saibaba, D.A. Brown, A. Alexendarian, SIAM/ASA Journal on Uncertainty Quantification, Vol. 7, No. 3, pp. 1105–1131, 2019.
51. "Parameter and Uncertainty Estimation for Dynamical Systems Using Surrogate Stochastic Processes," with M. Chung, M. Binois, R.B. Gramacy, D.J. Moquink, A.P. Smith, A.M Smith, SIAM Journal on Scientific Computing, Vol. 41, No. 4, A2212–A2238, 2019.
50. "A Metropolis-Hastings-within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems," with Tiangang Cui, 2017 MATRIX Annals, Editors: David R. Wood, Jan de Gier, Cheryl E. Praeger, Terence Tao. MATRIX Book Series, Volume 2, Springer, 2019.
49. "Point Spread Function Estimation in X-ray Imaging with Partially Collapsed Gibbs Sampling," with Kevin Joyce and Aaron Luttman, SIAM Journal on Scientific Computing, Vol. 40, No. 3, pp. B766--B787, 2018.
48. "L1-Regularized Inverse Problems for Image Deblurring via Bound and Equality Constrained Optimization", with Marylesa Howard, Research in Shape Analysis: Association for Women in Mathematics Series, vol. 12, Genctav et al. (eds), Springer, Cham, pp. 143-159, 2018.
47. "Bayesian inverse problems with l1 priors: a Randomize-then-Optimize approach," with Zheng Wang, Antti Solonen, Tiangang Cui, Youssef M. Marzouk, SIAM Journal on Scientific Computing, Vol. 39, No. 5, pp. S140-S166, 2017.
46. "A Metropolis-Hastings method for linear inverse problems with Poisson likelihood and Gaussian prior," with Aaron Luttman, International Journal of Uncertainty Quantification, Vol. 6, Iss. 1, pp. 35–55, 2016.
45. "Randomize-then-optimize for sampling and uncertainty quantification in electrical impedance tomography," with Aku Seppanen, Antti Solonen, Heikki Haario, and Jari Kaipio, SIAM Journal on Uncertainty Quantification, Vol. 3, pp. 1136–1158, 2015.
44. "Dealing with Boundary Artifacts in MCMC-Based Deconvolution," with Aaron Luttman, Linear Algebra and its Applications, vol. 473, pp. 339–358, 2015.
43. "Consequences of a refuge for the predator-prey dynamics of a wolf-elk system in Banff National Park, Alberta, Canada," with Joshua Goldberg and Mark Hebblewhite, PLoS ONE, 9(3), 2014: e91417. doi:10.1371/journal.pone.0091417.
42. "Analysis of the Gibbs sampler for hierarchical inverse problems," with Sergios Agapiou, Omiros Papaspiliopoulos, and Andrew M. Stuart, SIAM Journal on Uncertainty Quantification, vol. 2, iss. 1, pp. 511-544, 2014.
41. "Randomize-then-Optimize: a method for sampling from posterior distributions in nonlinear inverse problems," with Antti Solonen, Heikki Haario, and Marko Laine, SIAM Journal on Scientific Computing, Volume 36, Issue 4, pp. A1359-C399, 2014.
40. "Optimization-based Sampling for the Ensemble Kalman filter," with Antti Solonen, Alexander Bibov, and Heikki Haario, International Journal of Uncertainty Quantification, vol. 4, iss. 4, pp. 349-364, 2014.
39. "Efficient MCMC-Based Image Deblurring with Neumann Boundary Conditions," with Marylesa Howard and Jim Nagy, Electronic Transactions in Numerical Analysis, vol. 40, pp. 476 - 488, 2013.
38. "Gaussian Markov Random Field Priors for Inverse Problems," Inverse Problems and Imaging, vol. 7, no. 2, 2013, pp. 397 – 416.
37. "An ensemble Kalman filter using the conjugate gradient sampler", with Antti Solonen, Albert Parker, Heikki Haario, and Marylesa Howard, International Journal for Uncertainty Quantification, Vol. 3, No. 4, 2013, pp. 357–370.
36. "Krylov space approximate Kalman ltering," with Albert Parker, Antti Solonen, and Marylesa Howard, Numerical Linear Algebra with Applications, Vol. 20, 2013, pp. 171-184.
35. "Laplace-distributed increments, the Laplace prior, and edge-preserving regularization," Journal of Inverse and Ill-Posed Problems, Volume 20, Issue 3, 2012, pp. 271–285.
34. "MCMC-Based Image Reconstruction with Uncertainty Quantification," SIAM Journal on Scientific Computing, Vol. 34, No. 3, 2012, pp. A1316–A1332.
33. "An MCMC Method for Uncertainty Quantification in Nonnegativity Constrained Inverse Problems," with Colin Fox, Inverse Problems in Science and Engineering, Vol. 20, No. 4, 2012, pp. 477-498.
32. "A Computational Framework for Total Variation-Regularized Positron Emission Tomography", with John Goldes, Numerical Algorithms, 57(2), 2011, p. 255.
31. "Applications of a Nonnegatively Constrained Iterative Method with Statistically Based Stopping Rules to CT, PET, and SPECT Imaging," Electronic Transactions in Numerical Analysis, 38, 2011, pp. 34-43.
30. "Techniques for regularization parameter and hyper-parameter selection in PET and SPECT imaging", with John Goldes, Inverse Problems in Science and Engineering, 19(2), 2011, p. 267-280.
29. "Structured Linear Algebra Problems in Adaptive Optics Imaging", with Sarah Knepper and Jim Nagy, Advances in Computational Mathematics, vol. 5, issue 2-4, 2011, pp. 103-117.
28. "Hierarchical Regularization for Edge-Preserving Reconstruction of PET Images", with Daniela Calvetti and Erkki Somersalo, Inverse Problems, 26(3), 2010, 035010.
27. "An Iterative Method for Edge-Preserving MAP Estimation when Data-Noise is Poisson," with John Goldes, SIAM Journal on Scientific Computing, Vol.32, No.1, published online Feb 5, 2010.
26. "The variational Kalman filter and an efficient implementation using limited memory BFGS", with H. Auvinen, H. Haario, and T. Kauranne, Int. J. for Numerical Methods in Fluids, 64, 3, pp. 314--335, 2010.
25. "A Theoretical Framework for the Regularization of Poisson Likelihood Estimation Problems," Inverse Problems and Imaging, Vol. 4, No. 1, February 2010 p. 11-17.
24. "An Analysis of Regularization by Diffusion for Ill-Posed Poisson Likelihood Estimation," with N'djekornom Laobeul, Inverse Problems in Science and Engineering, Volume 17, Issue 4, June 2009 , pages 537 - 550.
23. "Total Variation-Penalized Poisson Likelihood Estimation for Ill-Posed Problems," with Aaron Luttman, Advances in Computational Mathematics, Volume 31, Issue 1, (2009), Page 35-59.
22. "Regularization Parameter Selection Methods for Ill-Posed Poisson Maximum Likelihood Estimation", with John Goldes, Inverse Problems, 25 (2009) 095005.
21. "Large-Scale Kalman Filtering Using the Limited Memory BFGS Method", with H. Auvinen, H. Haario, and T. Kauranne, Electronic Transactions in Numerical Analysis, Vol. 35, 2009, pp. 217-233.
20. "A Fixed Point Formulation of the k-Means Algorithm and a Connection to Mumford-Shaw", with Aaron Luttman, Applied Math E-Notes, vol. 9, 2009, pp. 274-276.
19. "Tikhonov Regularized Poisson Likelihood Estimation: Theoretical Justification and a Computational Method," with N'djekornom Laobeul, Inverse Problems in Science and Engineering, Volume 16, Issue 2 January 2008 , pages 199 - 215.
18. "The Stabilizing Properties of Nonnegativity Constraints in Least-Squares Image Reconstruction," with Jorma Merikoski and Roberto Vio, Int. J. of Pure and Applied Mathematics, vol. 43, no. 1, 2008, pp. 95-109.
17. "An Efficient Phase and Object Estimation Scheme for Phase-Diversity Time Series Data," IEEE Transactions on Image Processing, volume 17, issue 1, 2008, p. 9-15.
16. "An Analysis of Methods for Wavefront Reconstruction From Gradient Measurements in Adaptive Optics," Int. J. of Pure and Applied Mathematics, Vol. 42, No. 1, 2008, pp. 71-81.
15. "Wavefront Reconstruction Methods for Adaptive Optics Systems on Ground-Based Telescopes," SIAM Journal on Matrix Analysis and Application, Volume 30 Issue 1, 2008, pp. 67-83.
14. "Stopping Rules for a Nonnegatively Constrained Iterative Method for Ill-Posed Poisson Imaging Problems," BIT Numerical Mathematics, Volume 48, Number 4, December, 2008, pp. 651-664.
13. "An Efficient Computational Method for Total Variation-Penalized Poisson Likelihood Estimation," Inverse Problems and Imaging, vol. 2, no. 2, 2008, pp. 167 - 185.
12. "Wellposedness for Systems Arising in Time Domain Electromagnetics in Dielectrics," with H. T. Banks, Int. J. of Pure and Applied Mathematics 46 (2008), no. 1, 1-18.
11. "Analysis of Pattern Formation on the Surface of Respiring Leaves," with Aaron Luttman and Emily Stone, Physica D, Vol 232, Issue 2, 2007, pp. 142-155.
10. "A Variational Approach to Image Segmentation for Botanical Data," with Aaron Luttman, SIAM Journal on Scientific Computing, Vol 29, Issue 4, 2007, pp. 1550-1566.
This paper was featured in Science Magazine's Editors' Choice column. Erratum in SISC Vol 30, Issue 1, p. 548.
09. "A Computational Method for the Restoration of Images With an Unknown, Spatially-Varying Blur," with Stuart Jeffries, Jim Nagy and Bob Plemmons, Optics Express, vol. 14, Iss. 5, 2006, pp. 1767-1782.
08. "Covariance-Preconditioned Iterative Methods for Nonnegatively Constrained Astronomical Imaging," with Jim Nagy, SIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 4, 2006, pp. 1184-1198.
07. "Least-Squares methods with Poissonian noise: analysis and a comparison with the Richardson-Lucy algorithm," with R. Vio and W. Wamsteker, Astronomy and Astrophysics, 436, 2005, pp. 741-755.
06. "Dealing with edge effects in least-squares image deconvolution problems," with R. Vio, M. Donatelli, and W. Wamsteker, Astronomy and Astrophysics, vol. 442, pp. 397-403, 2005.
05. "A Nonnegatively Constrained Trust Region Algorithm for the Restoration of Images with an Unknown Blur," Electronic Transactions in Numerical Analysis, vol. 20, 2005, pp. 139-153.
04. "Parameter Identification for a Dispersive Dielectric in 2D Electromagnetics: Forward and Inverse Methodology with Statistical Considerations," with H. T. Banks, Int. J. of Computational and Numerical Analysis and Applications, vol. 5, No. 1, 2004, pp. 13-49.
03. "A Limited Memory, Quasi-Newton Preconditioner for Nonnegatively Constrained Image Reconstruction," Journal of the Optical Society of America A, vol. 21, no. 5, 2004, pp. 724-731.
02. "A Nonnnegatively Constrained Convex Programming Method for Image Reconstruction," with C.R. Vogel, SIAM Journal on Scientific Computing, vol. 25, no. 4, 2004, pp. 1326-1343.
01. "Computational Methods for a Large-Scale Inverse Problem Arising in Atmospheric Optics," with Luc Gilles and C.R. Vogel, Inverse Problems, 18, 2002, pp. 237-252.
July 2021–present Chair of the Department of Mathematical Sciences
June 2015–June 2017 Grievance Officer University Faculty Association Faculty Union, The University of Montana
August 2013–present Full Professor Department of Mathematical Sciences The University of Montana
August 2009–August 2013 Tenured Department of Mathematical Sciences The University of Montana
August 2008–August 2010 Co-Director Montana Ecology of Infectious Disease NSF-IGERT PhD Program The University of Montana
August 2007–August 2013 Associate Professor Department of Mathematical Sciences The University of Montana
August 2003–August 2007 Assistant Professor Department of Mathematical Sciences The University of Montana
August 2002–July 2003 Postdoctoral Fellow Statistical and Applied Mathematical Sciences Institute
August 2002–July 2003 Postdoctoral Fellow Center for Research in Scientific Computation, North Carolina State University
January 2019-June 2019, Visiting Professor and Gordon Preston Sabbatical Fellow, School of Mathematical Sciences, Monash University, Australia.
September 2018-January 2019, Visiting Professor, Department of Applied Mathematics and Computer Science, Technical University of Denmark.
Summer 2011-2014 (2-3 weeks/year), Visiting Professor, Division of Physical Sciences Lappeenranta University of Technology Lappeenranta, Finland
August 2010–June 2011 Visiting Professor, Department of Physics, The University of Otago Dunedin, New Zealand
August 2006–July 2007 Visiting Professor, Department of Mathematics and Statistics, The University of Helsinki Helsinki, Finland
Department of Mathematical Sciences
I love to read and relax at my property on the Dearborn River. I also love to mountain bike, ski, backpack, and climb local peaks.