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Subsampled First-Order Optimization Methods with Applications in Imaging

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

Author

Listed:
  • Stefania Bellavia

    (Università degli Studi di Firenze (INdAM-GNCS members), Dipartimento di Ingegneria Industriale)

  • Tommaso Bianconcini

    (Verizon Connect)

  • Nataša Krejić

    (Faculty of Sciences, University of Novi Sad, Department of Mathematics and Informatics)

  • Benedetta Morini

    (Università degli Studi di Firenze (INdAM-GNCS members), Dipartimento di Ingegneria Industriale)

Abstract

This work presents and discusses optimization methods for solving finite-sum minimization problems which are pervasive in applications, including image processing. The procedures analyzed employ first-order models for the objective function and stochastic gradient approximations based on subsampling. Among the variety of methods in the literature, the focus is on selected algorithms which can be cast into two groups: algorithms using gradient estimates evaluated on samples of very small size and algorithms relying on gradient estimates and machinery from standard globally convergent optimization procedures. Neural networks and convolutional neural networks widely used for image processing tasks are considered, and a classification problem of images is solved with some of the methods presented.

Suggested Citation

  • Stefania Bellavia & Tommaso Bianconcini & Nataša Krejić & Benedetta Morini, 2023. "Subsampled First-Order Optimization Methods with Applications in Imaging," 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 2, pages 61-95, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_78
    DOI: 10.1007/978-3-030-98661-2_78
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