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Frequency Analysis of Gradient Descent Method and Accuracy of Iterative Image Restoration

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Analysis of Images, Social Networks and Texts (AIST 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 542))

Abstract

For images with sharp changes of intensity, the appropriate regularization is based on variational functionals. In order to minimize such a functional, the gradient descent approach can be used. In this paper, we analyze the performance of the gradient descent method in the frequency domain and show that the method converges to the sum of the original undistorted function and the kernel function of a linear distortion operator.

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Acknowledgments

The work was supported by the Ministry of Education and Science of Russian Federation, grant 2.1766.2014К and RFBR grant 13.01.00735.

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Authors and Affiliations

  1. Research Laboratory, Chelyabinsk State University, Chelyabinsk, Russia

    Artyom Makovetskii, Alexander Vokhmintsev & Vitaly Kober

  2. Department of Computer Science, CICESE, Ensenada, B.C., Mexico

    Vitaly Kober

  3. Institute of Informatics Problems of RAS, Moscow, Russia

    Vladislav Kuznetsov

Authors
  1. Artyom Makovetskii
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  2. Alexander Vokhmintsev
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  3. Vitaly Kober
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  4. Vladislav Kuznetsov
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Corresponding author

Correspondence to Alexander Vokhmintsev .

Editor information

Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Mikhail Yu. Khachay

  2. Wolverhampton, United Kingdom

    Natalia Konstantinova

  3. Technische Universität Darmstadt, Darmstadt, Germany

    Alexander Panchenko

  4. National Research University Higher School of Economics, Moscow, Russia

    Dmitry Ignatov

  5. Ural Federal University, Yekaterinbug, Russia

    Valeri G. Labunets

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Makovetskii, A., Vokhmintsev, A., Kober, V., Kuznetsov, V. (2015). Frequency Analysis of Gradient Descent Method and Accuracy of Iterative Image Restoration. In: Khachay, M., Konstantinova, N., Panchenko, A., Ignatov, D., Labunets, V. (eds) Analysis of Images, Social Networks and Texts. AIST 2015. Communications in Computer and Information Science, vol 542. Springer, Cham. https://doi.org/10.1007/978-3-319-26123-2_11

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  • DOI: https://doi.org/10.1007/978-3-319-26123-2_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26122-5

  • Online ISBN: 978-3-319-26123-2

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