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Data-Informed Regularization for Inverse and Imaging Problems

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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Abstract

This chapter presents a new regularization method for inverse and imaging problems, called data-informed (DI) regularization, that implicitly avoids regularizing the data-informed directions. Our approach is inspired by and has a rigorous root in disintegration theory. We shall, however, present an elementary and constructive path using the classical truncated SVD and Tikhonov regularization methods. Deterministic and statistical properties of the DI approach are rigorously discussed, and numerical results for image deblurring, image denoising, and X-ray tomography are presented to verify our findings.

Submitted to the editors DATE.

This work was partially funded by the National Science Foundation awards NSF-1808576 and NSF-CAREER-1845799; by the Defense Threat Reduction Agency award DTRA-M1802962; by the Department of Energy award DE-SC0018147; by KAUST; by 2018 ConTex award; and by 2018 UT-Portugal CoLab award. The authors are grateful to the supports.

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Author information

Authors and Affiliations

  1. Department of Aerospace Engineering and Engineering Mechanics, UT Austin, Austin, TX, USA

    Jonathan Wittmer

  2. Department of Aerospace Engineering and Engineering Mechanics, The Oden Institute for Computational Engineering and Sciences, UT Austin, Austin, TX, USA

    Tan Bui-Thanh

Authors
  1. Jonathan Wittmer
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  2. Tan Bui-Thanh
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Corresponding authors

Correspondence to Jonathan Wittmer or Tan Bui-Thanh .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK

    Ke Chen

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Carola-Bibiane Schönlieb

  3. Hong Kong Center for Cerebrocardiovascular Health Engineering (COCHE), Shatin, Hong Kong

    Xue-Cheng Tai

  4. Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA

    Laurent Younes

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Wittmer, J., Bui-Thanh, T. (2023). Data-Informed Regularization for Inverse and Imaging Problems. In: Chen, K., Schönlieb, CB., Tai, XC., Younes, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-98661-2_77

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