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

chung_feature

Primary Research Interests:

  • Scientific Computing and Numerical Linear Algebra

  • Inverse Problems

  • High Performance Computing

  • Image Reconstruction

  • Imaging Applications

As a computational scientist, my research lies in the intersection of three areas:

  • mathematics,
  • computer science, and
  • scientific applications.

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.

  • Image Processing Applications:

    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, and super-resolution imaging. I also develop methods for tomographic imaging, where the goal is to reconstruct 3-D images from 2-D projection data.

  • Separable Nonlinear Problems:

    Some problems have special structure, in that they are linear in some variables and nonlinear in others. In this project, we develop numerical methods that can efficiently solve such problems. Applications from super-resolution and blind-deconvolution are considered.

  • Optimal Design of Filters:

    In many applications, image reconstructions have to be done quickly and expensive parameter choice methods may not be possible. In this project, calibration data is used in an empirical Bayes risk minimization framework to pre-compute spectral filters.

  • 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

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:

  • 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


    Some friends and colleagues:

    Michele Benzi at Emory University
    Matthias Chung at Virginia Tech
    Eric de Sturler at Virginia Tech
    Malena Espanol at University of Akron
    Eldad Haber at University of British Columbia, Canada
    Misha Kilmer at Tufts University
    Youssef Marzouk at MIT
    Jim Nagy at Emory University
    Esmond Ng at Lawrence Berkeley National Lab
    Linh Nguyen at University of Idaho
    Dianne O'Leary at University of Maryland, College Park
    Katrina Palmer at Appalachian State University
    Lothar Reichel at Kent State University
    Lars Ruthotto at Emory University
    Arvind Saibaba at North Carolina State University
    Ioannis Sechopoulos at Emory University
    Luis Tenorio at Colorado School of Mines
    Piotr Wendykier at Wolfram Research
    Chao Yang at Lawrence Berkeley National Lab