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Analysis of the gradient descent method in problems of the signals and images restoration

  • Representation, Processing, Analysis and Understanding of Images
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Abstract

This paper is concerned with the problem of the restoration of a signal distorted by a linear operator. Functions of two variables are described by variations of two types, viz., by the total variation and the linear variation. The total variation is a metric characteristic of a function, while the linear variation is a topological characteristic of a function. We consider a model based on the gradient descent method and the possibility of the application of the gradient descent method jointly with linear variation. Numerical simulation results are given on the recovery of a function distorted by an operator.

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Authors and Affiliations

  1. Chelyabinsk State University, ul. br. Kashirinykh 129, Chelyabinsk, 454080, Russia

    A. Makovetskii & V. Kober

  2. Department of Computer Science, Division of Applied Physics, CICESE, Carretera Ensenada-Tijuana No. 3918, Ensenada, B.C. 22860, Mexico

    V. Kober

Authors
  1. A. Makovetskii
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  2. V. Kober
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Correspondence to A. Makovetskii.

Additional information

This paper uses the materials of a report that was submitted at the 11th International Conference Pattern Recognition and Image Analysis: New Information Technologies that was held in Samara, Russia on September 23–28, 2013.

Artem Yu. Makovetskii. Born 1967. Graduated from the Chelyabinsk State University in 1992. Received Candidate’s degree in 2000. At present he is an associate professor at the Chelyabinsk State University. Scientific interests: digital processing of signals and images, pattern recognition. Author of 12 publications.

Vitalii I. Kober. Born 1961. Graduated from the Kuibushev Institute of Aviation in 1984. Received Candidate’s degree in 1992 and Doctor’s in 2004. At present he is a leading researcher at the Institute for Information Transmission Problems, Russian Academy of Sciences, and a professor at the Chelysbinsk state university. Scientific interests: processing of signals and images, pattern recognition. Author of more than 100 publications.

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Makovetskii, A., Kober, V. Analysis of the gradient descent method in problems of the signals and images restoration. Pattern Recognit. Image Anal. 25, 53–59 (2015). https://doi.org/10.1134/S1054661815010101

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  • DOI: https://doi.org/10.1134/S1054661815010101

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