DMS Applied Mathematics Seminar

Speaker: Mattias Chung (Virginia Tech)

Title: Computational Challenges of Inverse Problems

Abstract: Inverse problems are omnipresent in many scientific fields such as systems biology, engineering, medical imaging, and geophysics. The main challenges toward obtaining meaningful real-time solutions to large, data-intensive inverse problems are ill-posedness of the problem, large parameter dimensions, and/or complex model constraints. For instance, we consider iterative methods based on sampling for computing solutions to massive inverse problems where the entire dataset cannot be accessed or is not available all-at-once. Oftentimes, the selection of a proper regularization parameter is the most critical and computationally intensive task and may hinder real-time computations of the solution. For the linear problem, we describe a limited-memory sampled Tikhonov method, and for the nonlinear problem, we describe an approach to integrate the limited-memory sampled Tikhonov method within a nonlinear optimization framework. The proposed method is computationally efficient in that it only uses available data at any iteration to update both sets of parameters. Numerical experiments applied to massive super-resolution image reconstruction problems show the power of these methods. 

Short bio: Matthias (Tia) Chung is an Associate Professor in the Department of Mathematics at Virginia Tech and member of the Computational Modeling and Data Analytics division and the Systems Biology division in the Academy of Integrated Science. He joined the Virginia Tech in 2012, holds a Dipl. math. (Master of Science equivalent) from the University of Hamburg, Germany, and a Dr. rer. nat. (Ph.D. equivalent degree) in Computational Mathematics from the University of Lübeck, Germany. Before joining Virginia Tech, he was a Post-Doctoral Fellow at Emory University and Assistant Professor at Texas State University. Matthias Chung is an active member of the Society for Industrial and Applied Mathematics (SIAM) and its CSE, UQ, IS, and LA activity groups.

Matthias Chung’s research concerns various forms of cross-disciplinary inverse problems. Driven by its application, he and his lab develops and analyzes efficient numerical methods for inverse problems. Applications of interest include, but are not limited to, systems biology, medical and geophysical imaging, and dynamical systems. Challenges such as ill-posedness, large-scale, and uncertainty estimates are addressed by utilizing tools from and developing methods for regularization, randomized methods, stochastic learning, Bayesian inversion, and optimization. Research projects are supported by NSF, NIH, and USDA.