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Mathematics
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Mathematical Methods in Images and Signals Processing
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Mathematical Methods in Images and Signals Processing

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 9401

Special Issue Editors

Dr. Domenico Vitulano

E-Mail Website
Guest Editor
1. Sapienza – Rome University, SBAI Department, Via Antonio Scarpa 14, 00161 Rome, Italy
2. Istituto per le Applicazioni del Calcolo, Via dei Taurini 19, 00185 Rome, Italy
Interests: signal and image coding; pattern recognition; indexing and computer vision; visibility laws; wavelets; iterated function systems; variational models
Dr. Vittoria Bruni

E-Mail Website
Guest Editor
1. SBAI Department, Sapienza–Rome University, Via Antonio Scarpa 14, 00161 Rome, Italy
2. Istituto per le Applicazioni del Calcolo, Via dei Taurini 19, 00185 Rome, Italy
Interests: mathematical methods in images and signals processing

Special Issue Information

Dear Colleagues,

The fast and wide spread of new technologies has led the scientific community to develop new and more sophisticated mathematical models and methods to face the new challenges and needs coming from real applications involving signal and image processing.

The role of imaging is now fundamental in many fields, such as those involving smart acquisition devices. On the other hand, signal processing methods, like spectral analysis, time-frequency and time-scale representation, statistical signal processing, filtering, detection and estimation, and nonlinear signal processing, are successfully used in telecommunications systems.   

These approaches very often mainly aim at improving productivity as well as optimizing utilization and performance with a special emphasis on real-time implementations.

 

This Special Issue aims at bringing together researchers from different fields in order to present and share new theoretical results and advanced computational methods related to some of the current trends in signal and image processing. Theoretical models as well as applied mathematical methods oriented and/or based on real-world problems are welcome.

Dr. Domenico Vitulano
Assoc. Prof. Vittoria Bruni
Guest Editors

Manuscript Submission Information

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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. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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Published Papers (3 papers)

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Research

16 pages, 8250 KiB  
Article
Location of Multiple Damage Types in a Truss-Type Structure Using Multiple Signal Classification Method and Vibration Signals
by Carlos A. Perez-Ramirez, Jose M. Machorro-Lopez, Martin Valtierra-Rodriguez, Juan P. Amezquita-Sanchez, Arturo Garcia-Perez, David Camarena-Martinez and Rene de J. Romero-Troncoso
Mathematics 2020, 8(6), 932; https://doi.org/10.3390/math8060932 - 7 Jun 2020
Cited by 19 | Viewed by 3388
Abstract
A new multiple signal classification (MUSIC)-based methodology is presented for detecting and locating multiple damage types in a truss-type structure subjected to dynamic excitations. The methodology is based mainly on two steps: in step 1, the MUSIC method is employed to obtain the [...] Read more.
A new multiple signal classification (MUSIC)-based methodology is presented for detecting and locating multiple damage types in a truss-type structure subjected to dynamic excitations. The methodology is based mainly on two steps: in step 1, the MUSIC method is employed to obtain the pseudo-spectra of vibration signatures, healthy and damaged, to be used for damage detection. In step 2, a new damage index, based on the obtained pseudo-spectra, is proposed to measure the structure condition. Furthermore, the damage location is estimated according to the variation in the amplitudes of the estimated pseudo-spectra. The presented results show that the proposed methodology can make an accurate and reliable estimation of the condition and location of three specific damage conditions, i.e., loosened bolts, internal corrosion, and external corrosion. Full article
(This article belongs to the Special Issue Mathematical Methods in Images and Signals Processing)
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20 pages, 1207 KiB  
Article
A New Accelerated Viscosity Iterative Method for an Infinite Family of Nonexpansive Mappings with Applications to Image Restoration Problems
by Jenwit Puangpee and Suthep Suantai
Mathematics 2020, 8(4), 615; https://doi.org/10.3390/math8040615 - 16 Apr 2020
Cited by 9 | Viewed by 2269
Abstract
The image restoration problem is one of the popular topics in image processing which is extensively studied by many authors because of its applications in various areas of science, engineering and medical image. The main aim of this paper is to introduce a [...] Read more.
The image restoration problem is one of the popular topics in image processing which is extensively studied by many authors because of its applications in various areas of science, engineering and medical image. The main aim of this paper is to introduce a new accelerated fixed algorithm using viscosity approximation technique with inertial effect for finding a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and prove a strong convergence result of the proposed method under some suitable control conditions. As an application, we apply our algorithm to solving image restoration problem and compare the efficiency of our algorithm with FISTA method which is a popular algorithm for image restoration. By numerical experiments, it is shown that our algorithm has more efficiency than that of FISTA. Full article
(This article belongs to the Special Issue Mathematical Methods in Images and Signals Processing)
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17 pages, 5217 KiB  
Article
Vibration Signal Processing-Based Detection of Short-Circuited Turns in Transformers: A Nonlinear Mode Decomposition Approach
by Jose R. Huerta-Rosales, David Granados-Lieberman, Juan P. Amezquita-Sanchez, David Camarena-Martinez and Martin Valtierra-Rodriguez
Mathematics 2020, 8(4), 575; https://doi.org/10.3390/math8040575 - 13 Apr 2020
Cited by 15 | Viewed by 3035
Abstract
Transformers are vital and indispensable elements in electrical systems, and therefore, their correct operation is fundamental; despite being robust electrical machines, they are susceptible to present different types of faults during their service life. Although there are different faults, the fault of short-circuited [...] Read more.
Transformers are vital and indispensable elements in electrical systems, and therefore, their correct operation is fundamental; despite being robust electrical machines, they are susceptible to present different types of faults during their service life. Although there are different faults, the fault of short-circuited turns (SCTs) has attracted the interest of many researchers around the world since the windings in a transformer are one of the most vulnerable parts. In this regard, several works in literature have analyzed the vibration signals that generate a transformer as a source of information to carry out fault diagnosis; however this analysis is not an easy task since the information associated with the fault is embedded in high level noise. This problem becomes more difficult when low levels of fault severity are considered. In this work, as the main contribution, the nonlinear mode decomposition (NMD) method is investigated as a potential signal processing technique to extract features from vibration signals, and thus, detect SCTs in transformers, even in early stages, i.e., low levels of fault severity. Also, the instantaneous root mean square (RMS) value computed using the Hilbert transform is proposed as a fault indicator, demonstrating to be sensitive to fault severity. Finally, a fuzzy logic system is developed for automatic fault diagnosis. To test the proposal, a modified transformer representing diverse levels of SCTs is used. These levels consist of 0 (healthy condition), 5, 10, 15, 20, and 25 SCTs. Results demonstrate the capability of the proposal to extract features from vibration signals and perform automatic fault diagnosis. Full article
(This article belongs to the Special Issue Mathematical Methods in Images and Signals Processing)
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