"Seht ihr den Mond dort stehen?
Er ist nur halb zu sehen,
Und ist doch rund und schÃ¶n!
So sind wohl manche Sachen,
Die wir getrost belachen,
Weil unsre Augen sie nicht sehn."
Matthias Claudius (Abendlied, um 1778)
Research summary
My research interests concern various forms of inverse problems. Driven by its application, I develop and analyze efficient numerical methods for inverse problems. Applications of interest are, but not limited to, systems biology, medical and geophysical imaging, and dynamical systems.
Challenges for solving such problems include the high dimensionality of the problem, potential illposedness, and constraints enforced by its application. For instance, illposedness of inverse problems require prior knowledge and is usually integrated as regularization. I investigate such regularization methods to obtain meaningful solutions.
With respect to the inverse problem, I develop and investigate efficient optimization methods to overcome challenges such as constraints and discontinuity.
Methods for large scale inverse problems, such as problems from imaging applications, require special considerations methods. For instance, structure or low rank approximation are investigated to solve nearby problems efficiently. To quantify uncertainty in model and estimates, I utilize Bayes and empirical Bayes frameworks.
Estimating parameter for dynamical systems (ODE constraint optimization) can be particular challenging. I investigate robust parameter estimation methods to handle even chaotic systems.
Research keywords
inverse problems, computational biology & medicine, numerical analysis, optimization, optimal experimental design, scientific computing, regularization, applied linear algebra, dynamical systems.
Research group
 Justin Krueger
Justin Krueger's research interests lie in parameter estimation methods. In particular, he enjoys studying the limitations and computational efficiency of such methods and working to improve the methods on both fronts.
PhD student  Joseph Slagel
Big data inverse problems
PhD student  Taewon Cho
Medical image processing and large scale inverse problem
Master student  Robert Torrence
Uncertainty quantification in parameter estimates of ODEs
Master student  Bryan Kaperick
Randomized linear algebra
Undergraduate student  Miao Wang
Bayesian inversion for thermal cooling experiments
Undergraduate student
Alumni
Collaborators
Julianne Chung @ Virginia Tech
Britta Göbel @ SanofiAventis
Eldad Haber @ University of British Columbia
Brent Johnson @ University of Rochester
Qi Long @ Emory University
Dianne O'Leary @ University of Maryland
Kerstin Oltmanns @ University of Lübeck
Mihai Pop @ University of Maryland
Research awards

Ongoing

Virginia Tech Planning Grant: I/UCRC for Advanced Subsurface Earth Resource Models, NSF I/UCRC (1650463), PI,
Collaborators: Colorado School of Mines
Starting in 2017

Quantifying Nitrogen Transformations and Loses Associated With Manure Storage to Improve Accuracy of Whole Farm Process Based Nitrogen Accounting Models, USDA NIFA: 201608687, CoPI
Collaborators: Jactone Ogejo and Biswarup Mukhopadhyay
Starting in 2017

Completed

Identifying the dynamics of small and large microbial communities, NIH R21 (1R21GM10768301), PI
Collaborators: Mihai Pop
20132016

Optimal Experimental Design with Model Constraints, Texas State University Research Enhancement Grant, PI
20112012

Energy Metabolism: Physiology and Model, Computing in Medicine and Life Sciences, Graduate School of the German Research Association (DFG), PI
20072012

Clinical research group “The Selfish Brain”, funded by the German Research Association (DFG), I
20052008

Research center “Plasticity and Sleep”, funded by the German Research Association (DFG), I
20042005
Software tools
Optimal regularized inverse matrices (Matlab Implementation)
Descriptive Statistics (Matlab Implementation)
Iterative adaptive Simpson/Lobatto Method (Matlab Implementation)
Visualization for Spherical Harmonics (Matlab Implementation)
Continuous Shooting (Parameter Estimation for ODEs)