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Wavelets, Fractals and Information Theory IV

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

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 4596

Special Issue Editor


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Guest Editor
Engineering School (DEIM), University of Tuscia, Largo dell'Università, 01100 Viterbo, Italy
Interests: wavelets; fractals; fractional and stochastic equations; numerical and computational methods; mathematical physics; nonlinear systems; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Wavelet analysis, fractals, fractional order operators, and nonlinear methods for the solution of nonlinear, irregular problems are playing an increasing role in science, engineering applications, and information theory. Wavelet and fractals are the most suitable and efficient methods to analyze irregular shapes and signals, complex systems, localized functions, singularities and singular operators, non-differentiable functions, and, in general, nonlinear and singular problems. Nonlinearity and nonregularity usually characterize the complexity of a problem, thus representing the most studied features to approach a solution to complex problems. Wavelets, fractals, and fractional calculus might also help to improve the analysis of the complexity of a system by taking advantage of the scale dependence typical of wavelets and the recursive law typical of fractals, or the interpolation which is peculiar for fractional operators.

This Special Issue will also be an opportunity to extend the research fields of several interdisciplinary fields, such as image processing, the theory of differential/integral equations, number theory and special functions, generalized multiresolution analysis, and entropy as a measure in all aspects of the theoretical and practical studies of mathematics, physics, and engineering.

The main topics of this Special Issue include (but are not limited to):

  • Entropy encoding, wavelet compression, and information theory;
  • Fractals, non-differentiable functions. theoretical and applied analytical problems of fractal type, fractional equations;
  • Fractal and wavelet solutions of fractional differential equations;
  • Wavelet analysis, integral transforms, and applications;
  • Wavelet-fractal entropy encoding and computational mathematics in data analysis and time series, including in image analysis;
  • Wavelet-fractal approach;
  • Multiscale problems;
  • Stochastic problems;
  • Fractional order operators and methods;
  • Artificial Intelligence.

Prof. Dr. Carlo Cattani
Guest Editor

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.

Published Papers (2 papers)

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Research

13 pages, 433 KiB  
Article
Using Non-Additive Entropy to Enhance Convolutional Neural Features for Texture Recognition
by Joao Florindo and Konradin Metze
Entropy 2021, 23(10), 1259; https://doi.org/10.3390/e23101259 - 27 Sep 2021
Cited by 1 | Viewed by 1397
Abstract
Here we present a study on the use of non-additive entropy to improve the performance of convolutional neural networks for texture description. More precisely, we introduce the use of a local transform that associates each pixel with a measure of local entropy and [...] Read more.
Here we present a study on the use of non-additive entropy to improve the performance of convolutional neural networks for texture description. More precisely, we introduce the use of a local transform that associates each pixel with a measure of local entropy and use such alternative representation as the input to a pretrained convolutional network that performs feature extraction. We compare the performance of our approach in texture recognition over well-established benchmark databases and on a practical task of identifying Brazilian plant species based on the scanned image of the leaf surface. In both cases, our method achieved interesting performance, outperforming several methods from the state-of-the-art in texture analysis. Among the interesting results we have an accuracy of 84.4% in the classification of KTH-TIPS-2b database and 77.7% in FMD. In the identification of plant species we also achieve a promising accuracy of 88.5%. Considering the challenges posed by these tasks and results of other approaches in the literature, our method managed to demonstrate the potential of computing deep learning features over an entropy representation. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory IV)
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29 pages, 1014 KiB  
Article
Clifford Wavelet Entropy for Fetal ECG Extraction
by Malika Jallouli, Sabrine Arfaoui, Anouar Ben Mabrouk and Carlo Cattani
Entropy 2021, 23(7), 844; https://doi.org/10.3390/e23070844 - 30 Jun 2021
Cited by 12 | Viewed by 2348
Abstract
Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in [...] Read more.
Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. In the present paper, a wavelet/multiwavelet method is proposed to perfectly extract the fetal ECG parameters from the abdominal mother ECG. In a first step, due to the wavelet/mutiwavelet processing, a denoising procedure is applied to separate the noised parts from the denoised ones. The denoised signal is assumed to be a mixture of both the MECG and the FECG. One of the well-known measures of accuracy in information processing is the concept of entropy. In the present work, a wavelet/multiwavelet Shannon-type entropy is constructed and applied to evaluate the order/disorder of the extracted FECG signal. The experimental results apply to a recent class of Clifford wavelets constructed in Arfaoui, et al. J. Math. Imaging Vis. 2020, 62, 73–97, and Arfaoui, et al. Acta Appl. Math. 2020, 170, 1–35. Additionally, classical Haar–Faber–Schauder wavelets are applied for the purpose of comparison. Two main well-known databases have been applied, the DAISY database and the CinC Challenge 2013 database. The achieved accuracy over the test databases resulted in Se = 100%, PPV = 100% for FECG extraction and peak detection. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory IV)
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