Click here and scroll down to watch a 5 minute introduction to my research

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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 ill-posed inverse problems

    Most inverse problems are ill-posed, 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 large-scale 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 super-resolution and blind-deconvolution 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, super-resolution imaging, and inverse modeling. I also develop methods for tomographic imaging, where the goal is to reconstruct 3-D (or 4-D) images from observed projection data.

  • Large Scale Problems

    Achieving high resolution images often requires high-performance 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 Golub-Kahan based hybrid methods for solving ill-posed inverse problems.

Optimal Regularized Inverse Matrices (ORIMs): This repository contains MATLAB files for computing low-rank 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:

  • Click here to watch a talk I gave at the 2009 DOE CSGF Conference.
    ** This talk is suitable for a general science audience. **

  • Listen to an audio recording from my talk at the 2020 SAMSI Numerical Analysis in Data Science Opening Workshop: Computational Advancements in Large-Scale Inverse Problems

  • Listen to an audio recording from my talk at the 2017 SIAM Computational Science and Engineering Conference: Generalized Hybrid Iterative Methods for Large-Scale Bayesian Inverse Problems

  • Listen to audio recordings from my minisymposia at the 2015 SIAM Applied Linear Algebra Meeting. Thanks to all my co-organizers and to all the speakers!
  • I was a guest lecturer at the IMA New Directions Short Course: Introduction to Uncertainty Quantification, June 15-26, 2015

  • Listen to audio recordings from my minisymposium on Computational Methods for Inverse Problems in Imaging at the 2014 SIAM Annual Meeting. Thanks to all the speakers and to the SIAM Activity Group on Linear Algebra for sponsoring the session. A direct link to my talk: Optimal Regularization Parameter for General-form Tikhonov Regularization


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    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.

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    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.
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    Some Links