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Inverse Problems: Advanced Methods and Innovative Applications

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: 30 June 2025 | Viewed by 332

Special Issue Editors


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Guest Editor
1. Consorzio RFX (CNR, ENEA, INFN, University of Padova, Acciaierie Venete SpA), C.so Stati Uniti 4, 35127 Padova, Italy
2. Istituto per la Scienza e la Tecnologia dei Plasmi, CNR, Padova, Italy
Interests: nuclear fusion; entropy; information theory; machine learning; evolutionary computation; tomography; image processing
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
National Institute for Laser, Plasma and Radiation Physics, RO-077125 Magurele-Bucharest, Romania
Interests: computed tomography; imagine processing; time series analysis; complex networks; data mining; Monte Carlo simulations
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Department of Industrial Engineering, Università degli Studi di Roma Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy
Interests: numerical analysis; data analysis

Special Issue Information

Dear Colleagues,

Inverse problems arise from the need to obtain information about unknown phenomena or objects from indirect measurements. While the goal of collecting data entails gaining meaningful information about the phenomena under study, in many situations, the quantities that can be measured are different from those of interest. Solving "inverse problems" requires exploiting the results of actual observations to infer the values of the parameters characterizing the system under investigation. In broad terms, an inverse problem can be defined as the determination of causes from the measurement of effects.

Inverse problems are typically difficult to solve for at least three different reasons: (1) often they are ill-posed, in the sense that distinct causes can account for the same effect and small changes in a perceived effect can correspond to very large changes in a given cause; (2) the exploration of huge parameter spaces may be necessary to identify the values of the model’s parameters; and (3) the data can be affected by noise uncertainties, exacerbating the previous two issues.

Despite these difficulties, inverse problems are extremely important in the applied sciences, because very often they are the only way to obtain information about entities that cannot be measured directly. Indeed, their applications range from medical imaging and industrial process monitoring to remote sensing, astrophysics, and the modelling of financial markets.

This Special Issue aims to collect papers that describe new solutions to inverse problems. Both theoretical advances and innovative applications are within its scope. Approaches involving artificial intelligence solutions are particularly welcome. Please be advised that military applications of inverse problems will be rejected.

These contributions could be based on (but are not limited to) the following fields:

  • Parameter estimation;
  • Bayesian statistics;
  • Machine learning;
  • Neural computation;
  • Genetic programming;
  • Image processing;
  • Information theory;
  • Network theory.

Dr. Andrea Murari
Dr. Teddy Craciunescu
Dr. Ivan Wyss
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • parameter estimation
  • Bayesian statistics
  • machine learning
  • neural computation
  • genetic programming
  • image processing
  • information theory
  • network theory

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Published Papers (1 paper)

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Research

18 pages, 1062 KiB  
Article
Investigation of the Internal Structure of Hard-to-Reach Objects Using a Hybrid Algorithm on the Example of Walls
by Rafał Brociek, Józef Szczotka, Mariusz Pleszczyński, Francesca Nanni and Christian Napoli
Entropy 2025, 27(5), 534; https://doi.org/10.3390/e27050534 - 16 May 2025
Viewed by 37
Abstract
The article presents research on the application of computed tomography with an incomplete dataset to the problem of examining the internal structure of walls. The case of incomplete information in computed tomography often occurs in various applications, e.g., when examining large objects or [...] Read more.
The article presents research on the application of computed tomography with an incomplete dataset to the problem of examining the internal structure of walls. The case of incomplete information in computed tomography often occurs in various applications, e.g., when examining large objects or when examining hard-to-reach objects. Algorithms dedicated to this type of problem can be used to detect anomalies (defects, cracks) in the walls, among other artifacts. Situations of this type may occur, for example, in old buildings, where special caution should be exercised. The approach presented in the article consists of a non-standard solution to the problem of reconstructing the internal structure of the tested object. The classical approach involves constructing an appropriate system of equations based on X-rays, the solution of which describes the structure. However, this approach has a drawback: solving such systems of equations is computationally very complex, because the algorithms used, combined with incomplete information, converge very slowly. In this article, we propose a different approach that eliminates this problem. To simulate the structure of the tested object, we use a hybrid algorithm that is a combination of a metaheuristic optimization algorithm (Group Teaching Optimization Algorithm) and a numerical optimization method (Hook-Jeeves method). In order to solve the considered inverse problem, a functional measuring the fit of the model to the measurement data is created. The hybrid algorithm presented in this paper was used to find the minimum of this functional. This paper also shows computational examples illustrating the effectiveness of the algorithms. Full article
(This article belongs to the Special Issue Inverse Problems: Advanced Methods and Innovative Applications)
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