Mathematical Methods for Image Processing and Understanding

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 10 May 2025 | Viewed by 1117

Special Issue Editors


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Guest Editor
Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy
Interests: real analysis, theory of integral operators, approximation theory, and their applications to signal and image processing and reconstruction

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Guest Editor
Department of Mathematics and Computer Science, University of Perugia, I-06123 Perugia, Italy
Interests: image processing; numerical linear algebra; computational complexity

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Guest Editor Assistant
Department of Mathematics and Computer Science “U.Dini”-DIMAI, University of Florence, 67/a, Viale Giovanni Battista Morgagni, 50134 Firenze, Italy
Interests: real analysis; theory of integral operators; approximation theory and their applications to signal and image processing and reconstruction

Special Issue Information

Dear Colleagues,

We are very happy to announce that The Workshop on Mathematical Methods for Image Processing and Understanding (https://sites.google.com/view/mmipu-2023/home-page) will be held in conjunction with the 2023 International Conference on Computational Science and its Applications (ICCSA 2023) in Athens, Greece, on July 3‒6, 2023.

The Workshop is focused on the analysis of mathematical methods to solve the theoretical and computational problems that are typical in image processing and understanding. The themes and topics include but are not limited to:

  • Theoretical and numerical approximation for image processing;
  • Filter theory;
  • Space color definition;
  • Regularization techniques;
  • MAP estimation for image processing;
  • Image reconstruction;
  • Image enhancement;
  • Image rescaling;
  • Image segmentation;
  • Image registration;
  • Image clustering;
  • Image compactification;
  • Image demosaicing;
  • Medical imaging;
  • Digital tomography;
  • Mathematical methods for virtual document restoration;
  • Pattern recognition;
  • Stereoscopic and optical flow.

Moreover, applications of digital image processing in different fields will be also considered.

We would like to invite authors to submit an extended version of their conference papers for this Special Issue. All papers accepted in this Special Issue will meet the usual standards for publication in Mathematics.

Prof. Dr. Gianluca Vinti
Prof. Dr. Ivan Gerace
Guest Editors

Arianna Travaglini
Guest Editor Assistant

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Keywords

  • image processing
  • feature extraction and selection
  • pattern recognition
  • mathematical methods
  • regularization techniques
  • inverse problems in imaging

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Published Papers (1 paper)

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Research

21 pages, 507 KiB  
Article
A Note on the Convergence of Multigrid Methods for the Riesz–Space Equation and an Application to Image Deblurring
by Danyal Ahmad, Marco Donatelli, Mariarosa Mazza, Stefano Serra-Capizzano and Ken Trotti
Mathematics 2024, 12(12), 1916; https://doi.org/10.3390/math12121916 - 20 Jun 2024
Cited by 1 | Viewed by 540
Abstract
In recent decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on multigrid methods for a Riesz–Space FDE whose theoretical [...] Read more.
In recent decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on multigrid methods for a Riesz–Space FDE whose theoretical convergence analysis of such multigrid methods is currently limited in the relevant literature to the two-grid method. Here we provide a detailed theoretical convergence study in the multilevel setting. Moreover, we discuss its use combined with a band approximation and we compare the result with both τ and circulant preconditionings. The numerical tests include 2D problems as well as the extension to the case of a Riesz–FDE with variable coefficients. Finally, we investigate the use of a Riesz–Space FDE in a variational model for image deblurring, comparing the performance of specific preconditioning strategies. Full article
(This article belongs to the Special Issue Mathematical Methods for Image Processing and Understanding)
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