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Stabilizing deep tomographic reconstruction: Part B. Convergence analysis and adversarial attacks.

Weiwen Wu1,2,3, Dianlin Hu4, Wenxiang Cong1

  • 1Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA.

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Summary
This summary is machine-generated.

Deep image reconstruction networks are unstable due to lack of kernel awareness. We introduce the bounded relative error norm (BREN) property and analyze the analytic compressed iterative deep (ACID) scheme for improved stability and convergence.

Keywords:
analytic compressed iterative deep frameworkbounded relative error normcompressed sensingdeep reconstruction networkinstabilitykernel awareness

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Area of Science:

  • Image reconstruction
  • Deep learning
  • Mathematical analysis

Background:

  • Popular deep image reconstruction networks lack kernel awareness, leading to instability.
  • Lipschitz continuity is a key property for network stability.

Purpose of the Study:

  • Introduce the bounded relative error norm (BREN) property to enhance network stability.
  • Analyze the convergence and stability of the analytic compressed iterative deep (ACID) scheme.
  • Evaluate the robustness of reconstruction networks and the ACID workflow against adversarial attacks.

Main Methods:

  • Introduce the bounded relative error norm (BREN), a specific case of Lipschitz continuity.
  • Conduct a convergence study of the analytic compressed iterative deep (ACID) scheme.
  • Employ heuristic and mathematically rigorous analyses for convergence.
  • Develop adversarial attack algorithms to test network and workflow robustness.

Main Results:

  • The bounded relative error norm (BREN) property enhances network stability.
  • The analytic compressed iterative deep (ACID) scheme demonstrates convergence.
  • Numerical analysis confirms the ACID iteration's convergence regarding Lipschitz constant and local stability against noise.

Conclusions:

  • The BREN property offers a solution to instability in deep image reconstruction networks.
  • The ACID scheme provides a stable and convergent approach for image reconstruction.
  • The study validates the ACID workflow's resilience and numerical stability.