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Multiparameter Approaches in Image Processing

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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Abstract

Natural images often exhibit a highly complex structure that is difficult to describe using a single regularization term. Instead, many variational models for image restoration rely on different regularization terms in order to capture the different components of the image in question. While the resulting multipenalty approaches have in principle a greater potential for accurate image reconstructions than single-penalty models, their practical performance relies heavily on a good choice of the regularization parameters. In this chapter, we provide a brief overview of existing multipenalty models for image restoration tasks. Moreover, we discuss different approaches to the problem of multiparameter selection. For the numerical examples, we will focus on the balanced discrepancy principle and the L-hypersurface method applied to PDE-based image denoising problems.

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Author information

Authors and Affiliations

  1. NTNU, Trondheim, Norway

    Markus Grasmair

  2. Machine Intelligence Department, Simula Consulting and SimulaMet, Oslo, Norway

    Valeriya Naumova

Authors
  1. Markus Grasmair
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  2. Valeriya Naumova
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Corresponding authors

Correspondence to Markus Grasmair or Valeriya Naumova .

Editor information

Editors and Affiliations

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

    Ke Chen

  2. Dept Appl Math & Theoretical Phys, University of Cambridge, Cambridge, UK

    Carola-Bibiane Schönlieb

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Xue-Cheng Tai

  4. Department of Applied Mathematics & Stat, Johns Hopkins University, Baltimore, MD, USA

    Laurent Younces

Section Editor information

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

    Ke Chen Ph.D

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    Xuecheng Tai Ph.D

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

    Carola Schönlieb Ph.D

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

    Laurent Younes

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Grasmair, M., Naumova, V. (2022). Multiparameter Approaches in Image Processing. In: Chen, K., Schönlieb, CB., Tai, XC., Younces, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-03009-4_69-1

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  • DOI: https://doi.org/10.1007/978-3-030-03009-4_69-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03009-4

  • Online ISBN: 978-3-030-03009-4

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