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Data-Informed Regularization for Inverse and Imaging Problems

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author

Listed:
  • Jonathan Wittmer

    (UT Austin, Department of Aerospace Engineering and Engineering Mechanics)

  • Tan Bui-Thanh

    (The Oden Institute for Computational Engineering and Sciences, UT Austin, Department of Aerospace Engineering and Engineering Mechanics)

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.

Suggested Citation

  • Jonathan Wittmer & Tan Bui-Thanh, 2023. "Data-Informed Regularization for Inverse and Imaging Problems," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 35, pages 1235-1272, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_77
    DOI: 10.1007/978-3-030-98661-2_77
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