Click here and scroll down to watch a 5 minute introduction to my research
Primary Research Interests:
 Computational Inverse Problems
 Scientific Computing and Numerical Linear Algebra
 Uncertainty Quantification
 Data Science and Machine Learning
 Image Reconstruction and Applications
 High Performance Computing
Some research projects:
Regularization for illposed inverse problems
Most inverse problems are illposed, meaning small changes in the data can lead to large changes in the solution. Regularization is an approach to modify the problem and overcome this instability. My research on regularization includes spectral filtering, variational methods, hybrid approaches, and parameter selection methods.
See a recent survey paper: Julianne Chung and Silvia Gazzola. "Computational methods for largescale inverse problems: A survey on hybrid projection methods." arXiv: 2105.07221
New frameworks for regularization and uncertainty quantification
We develop new frameworks for regularization and advanced diagnostics (e.g., statistical tools) for error analysis and uncertainty quantification (UQ).
Stochastic approximation methods for massive problems
We develop iterative sampling methods with convergence theory to handle problems with massive datasets. Applications include machine learning for deep networks and streaming problems.

Separable Nonlinear Problems
Some problems have special structure, in that they are linear in some variables and nonlinear in others. We develop numerical methods that can efficiently solve such problems. Applications from superresolution and blinddeconvolution are considered.
Applications in Science and Engineering
Applications such as geophysics, molecular biology, astronomy, and medicine rely heavily on good imaging devices. Some problems that I work on include image deblurring, image denoising, superresolution imaging, and inverse modeling. I also develop methods for tomographic imaging, where the goal is to reconstruct 3D (or 4D) images from observed projection data.
Large Scale Problems
Achieving high resolution images often requires highperformance computing capabilities. In my research, I am not only interested in developing numerical algorithms, but also efficient implementations for distributed architectures.
Software
Click here for my GitHub page
HyBR: Efficient implementations of GolubKahan based hybrid methods for solving illposed inverse problems.
Optimal Regularized Inverse Matrices (ORIMs): This repository contains MATLAB files for computing lowrank ORIMs and ORIM updates as described in the paper:
Julianne Chung and Matthias Chung. Optimal Regularized Inverse Matrices for Inverse Problems, arXiv:1511169, 2016.
Quantitative
Susceptibility Mapping (QSM) Reconstruction : This repository contains MATLAB files for image deblurring and Quantitative
Susceptibility Mapping used in the review paper:
J.Chung, L.Ruthotto, Computational Methods for Image Reconstruction, NMR Biomedicine Special Issue: QSM, 2016
Online Audio Recordings:
** This talk is suitable for a general science audience. **
 Recent Advances in Numerical Linear Algebra for Inverse Problems Part I
 Recent Advances in Numerical Linear Algebra for Inverse Problems Part II
 A Celebration in Honor of Dianne P. O'Leary on the Occasion of her Retirement Part I
 A Celebration in Honor of Dianne P. O'Leary on the Occasion of her Retirement Part II
 A direct link to my talk: A Hybrid LSMR Algorithm for LargeScale Tikhonov Regularization
If you are an undergraduate or graduate student interested in research in any of these or related areas, please send me an email at jmchung@vt.edu. I am happy to meet with you to discuss research opportunities.
Many of my projects include interdisciplinary collaboration with scientists from various departments such as mathematics, computer science, radiology, and engineering. Please contact me if you are interested in potential collaborations.
Some Links
 AWM (Association for Women in Mathematics)
 SIAM (Society for Industrial and Applied Mathematics)
 AMS (American Mathematical Society)