Research

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Master's research

Deep neural networks for inverse problems in imaging

In the past decade, deep learning has been incredibly successful in a myriad of image processing applications. As a result, there has been growing interest in applying deep learning to solve inverse problems in imaging. For example, deep learning is being leveraged in medical imaging to optimize sampling (to reduce scan times or radiation dose) and speed up reconstruction and inference. Being able to tackle imaging problems is fundamental to the progress of science, engineering and medicine. Despite recent work indicating that deep learning performs better than state-of-the-art model-based methods for imaging, deep neural networks have significant issues with stability and generalization. This raises the key question: can we construct deep neural networks for inverse problems in imaging with state-of-the-art performance guarantees?

My supervisor Ben Adcock and I contribute towards answering this question by extending the work of Matthew Colbrook, et al. In a paper, we construct neural networks that achieve the same performance guarantees as state-of-the-art model-based methods to recover a class of analysis-sparse signals. In my master's thesis, recovery of gradient-sparse signals is considered instead. The neural network constructions are based on unrolling an optimization algorithm, which are made efficient by applying a restart scheme to accelerate the image reconstruction. This has led to interesting side work with Ben Adcock and Matthew Colbrook to examine general parameter-free restart schemes for continuous optimization.

Our work brings together several areas of mathematics, including convex optimization, compressed sensing, random matrix theory and deep learning.

Publications

Journal papers

• Ben Adcock, Matthew Colbrook & Maksym Neyra-Nesterenko
  Restarts subject to approximate sharpness: a parameter-free and optimal scheme for first-order methods
  Foundations of Computational Mathematics, 2025.
  article preprint
• Maksym Neyra-Nesterenko & Ben Adcock
  NESTANets: stable, accurate and efficient neural networks for analysis-sparse inverse problems
  Sampling Theory, Signal Processing, and Data Analysis, 21:4, 2023.
  article preprint

Abstracts

• Ben Adcock & Maksym Neyra-Nesterenko
  Provably accurate, stable and efficient deep neural networks for compressive imaging
  In: International Conference on Computational Harmonic Analysis, 2021.
  repository pdf

Theses and dissertations

• Maksym Neyra-Nesterenko
  Unrolled NESTA: constructing stable, accurate and efficient neural networks for gradient-sparse imaging problems
  MSc thesis, Simon Fraser University, 2023.
  repository

Presentations

• Parameter-free and optimal restart schemes for first-order methods via approximate sharpness
  WCOM Autumn - contributed talk
  University of British Columbia, Vancouver, BC, CA (Sep 21, 2024)
  slides
• Unrolled NESTA: constructing stable, accurate and efficient neural networks for gradient-sparse imaging problems
  Math Grad Social - seminar presentation
  Simon Fraser University, Burnaby, BC, CA (Feb 7, 2023)
  
• Restart schemes: a powerful parameter-free acceleration scheme for first-order methods
  SFU Applied Math Seminar - seminar presentation
  Simon Fraser University, Burnaby, BC, CA (Nov 23, 2022)
  
• Stable, accurate and efficient deep neural networks for reconstruction of gradient-sparse images
  SIAM Pacific Northwest Conference - minisymposium talk
  Washington State University, Vancouver, WA, US (May 21, 2022)
  
• Stable, accurate and efficient deep neural networks for gradient sparse imaging
  SIAM Conference on Imaging Science (IS22) - minisymposium talk
  Virtual (Mar 22, 2022)
  
• Stable, accurate and efficient deep neural networks for inverse problems with analysis sparse models
  SFU Operations Research Seminars - seminar presentation
  Virtual (Feb 14, 2022)
  
• Provably accurate, stable and efficient deep neural networks for compressive imaging
  International Conference on Computational Harmonic Analysis (ICCHA) - contributed talk
  Virtual (Sep 17, 2021)
  
• Provably accurate and stable deep neural networks for imaging
  CAIMS Annual Meeting - contributed talk
  Virtual (Jun 23, 2021)
  
• Provably accurate and stable deep neural networks for imaging
  Ottawa Mathematics Conference (OMC) - contributed talk
  Virtual (May 28, 2021)