Research

Computational foundations for next-generation imaging

My research focuses on extracting meaningful information from limited and imperfect measurements. I organize my work around three connected themes: numerical methods for large-scale inverse problems, physics + learning for reliable reconstruction, and biomedical & scientific imaging. Together, these themes connect advances in numerical computation with new capabilities in computational imaging.

My long-term vision is to develop the computational foundations for next-generation imaging systems that integrate mathematical structure, physical models, and data-driven learning. I am particularly interested in jointly recovering images and latent imaging parameters from incomplete measurements, pushing the limits of what can be resolved, tracked, and quantified.

Research vision: mathematical structure, imaging physics, and data-driven learning combine into computational imaging to resolve, track, and quantify
Computational imaging at the intersection of numerical methods, physics, and learning.
1 · Numerical Methods

Exploiting mathematical structure for efficient and reliable large-scale computation.
2 · Physics + Learning

Combining physical models with data-driven learning for interpretable reconstruction.
3 · Biomedical & Scientific Imaging

Extracting meaningful information from complex measurements.
Theme 1

Numerical Methods

Exploiting mathematical structure for efficient and reliable large-scale computation.

Modern inverse problems often involve high-dimensional variables, nonlinear forward models, incomplete data, and complex physical models, posing fundamental challenges in both computation and reliability. My research develops numerical methods that exploit mathematical and problem structure to address these challenges efficiently and reliably.

My work draws broadly on numerical analysis, scientific computing, and optimization. A recurring principle is to identify exploitable structure—across scales, curvature, low-dimensional representations, or forward models—and incorporate it directly into algorithm design. This perspective enables efficient computation for inverse problems that would otherwise be prohibitively expensive to solve.

Focus areas

  • Multigrid and multilevel methods
  • Quasi-Newton and proximal methods
  • Krylov-subspace methods and preconditioning
  • Stochastic and mini-batch optimization
  • Acceleration and extrapolation methods

Related publications

  1. [1] T. Hong, U. Villa, and J. A. Fessler, “A Convergent Generalized Krylov Subspace Method for Compressed Sensing MRI Reconstruction with Gradient-Driven Denoisers,” IEEE Transactions on Computational Imaging, vol. 12, pp. 378–390, Jan. 2026.
  2. [2] T. Hong, T.-an Pham, I. Yavneh, and M. Unser, “A Mini-Batch Quasi-Newton Proximal Method for Constrained Total-Variation Nonlinear Image Reconstruction,” SIAM Journal on Imaging Sciences, vol. 19, no. 3, pp. 1864–1894, 2026.
  3. [3] T. Hong, Z. Xu, J. Hu, and J. A. Fessler, “Using Randomized Nyström Preconditioners to Accelerate Variational Image Reconstruction,” IEEE Transactions on Computational Imaging, vol. 11, pp. 1630–1643, Oct. 2025.
  4. [4] T. Hong and I. Yavneh, “On Adapting Nesterov’s Scheme to Accelerate Iterative Methods for Linear Problems,” Numerical Linear Algebra with Applications, vol. 29, no. 2, p. e2417, 2022.
  5. [5] T. Hong, I. Yavneh, and M. Zibulevsky, “Merging Multigrid Optimization with SESOP.” 2018. Available at: https://arxiv.org/abs/1812.06896
Theme 2

Physics + Learning for Computational Imaging

Combining physical models with data-driven learning for interpretable reconstruction.

Computational imaging provides explicit knowledge of how measurements are physically generated, while data-driven learning can capture complex image structure from data. My research brings these complementary sources of information together within model-based reconstruction.

I am particularly interested in integrating learning with physical forward models, using learned priors, denoisers, and other data-driven representations to model image structure that is difficult to characterize explicitly. This integration allows learned information to guide reconstruction while maintaining consistency with the measurements and underlying imaging physics.

Focus areas

  • Learned priors
  • Physics-integrated iterative reconstruction
  • Convergence and reliability of learning-based methods

Related publications

  1. [1] T. Hong, U. Villa, and J. A. Fessler, “A Convergent Generalized Krylov Subspace Method for Compressed Sensing MRI Reconstruction with Gradient-Driven Denoisers,” IEEE Transactions on Computational Imaging, vol. 12, pp. 378–390, Jan. 2026.
  2. [2] T. Hong, Z. Xu, S. Y. Chun, L. Hernandez-Garcia, and J. A. Fessler, “Convergent Complex Quasi-Newton Proximal Methods for Gradient-Driven Denoisers in Compressed Sensing MRI Reconstruction,” IEEE Transactions on Computational Imaging, vol. 11, pp. 1534–1547, Oct. 2025.
  3. [3] T. Hong, X. Xu, J. Hu, and J. A. Fessler, “Provable Preconditioned Plug-and-Play Approach for Compressed Sensing MRI Reconstruction,” IEEE Transactions on Computational Imaging, vol. 10, pp. 1476–1488, Oct. 2024.
  4. [4] T. Hong, I. Yavneh, and M. Zibulevsky, “Solving RED with Weighted Proximal Methods,” IEEE Signal Processing Letters, vol. 27, pp. 501–505, Mar. 2020.
Theme 3

Biomedical & Scientific Imaging

Extracting meaningful information from complex measurements across MRI, photoacoustic, and optical imaging.

Biomedical and scientific imaging increasingly seek to recover information that is not directly accessible from measured data, from high-resolution anatomical structure to dynamic and quantitative information. My research develops computational imaging methods that expand what can be resolved, tracked, and quantified from limited and imperfect measurements.

I work across magnetic resonance imaging, photoacoustic, and optical imaging, where different measurement physics give rise to distinct inverse problems and computational challenges. Across these modalities, I am particularly interested in enabling faster and more robust imaging, resolving dynamic processes, and advancing quantitative imaging to better characterize underlying physical and physiological systems.

Magnetic Resonance Imaging

  • Accelerated and compressed-sensing MRI
  • Nonlinear and model-based reconstruction
  • Motion-robust reconstruction
My brain — 3D slice walkthrough
Movie of my brain.

Photoacoustic Imaging

  • Dynamic image reconstruction
  • Low-dimensional representations of spatiotemporal images
Photoacoustic computed tomography — vascular and volumetric imaging
Human chest vasculature and a 3D MOBY mouse phantom for photoacoustic imaging.

Optical Imaging

  • Optical diffraction tomography and Fourier ptychography
  • Nonlinear image reconstruction
  • Wave-based inverse problems
Optical diffraction tomography — principle and reconstruction results
Optical diffraction tomography — imaging model and 3D reconstruction.

Related publications

  1. [1] T. Hong, T.-an Pham, I. Yavneh, and M. Unser, “A Mini-Batch Quasi-Newton Proximal Method for Constrained Total-Variation Nonlinear Image Reconstruction,” SIAM Journal on Imaging Sciences, vol. 19, no. 3, pp. 1864–1894, 2026.
  2. [2] T. Hong, X. Xu, J. Hu, and J. A. Fessler, “Provable Preconditioned Plug-and-Play Approach for Compressed Sensing MRI Reconstruction,” IEEE Transactions on Computational Imaging, vol. 10, pp. 1476–1488, Oct. 2024.
  3. [3] T. Hong, J. Shah, L. Lozenski, R. Cam, M. Anastasio, and U. Villa, “A Virtual Imaging Framework for DCE-PACT Estimation of Tumor Perfusion,” in Medical Imaging: Physics of Medical Imaging, SPIE, 2026.
  4. [4] T. Hong, T.-an Pham, E. Treister, and M. Unser, “Diffraction Tomography with Helmholtz Equation: Efficient and Robust Multigrid-Based Solver.” 2021. Available at: https://arxiv.org/abs/2107.03679

Full list: Publications · Google Scholar