Special Issue "Recent Developments in Wavelet Transforms and Their Applications"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (30 September 2017).

Special Issue Editors

Prof. Dr. Lokenath Debnath
Website
Guest Editor
School of Mathematical and Statistical Sciences, College of Sciences, The University of Texas Rio Grande Vally, 1201 West University Dr. Edinburg, Texas 78539, USA
Interests: applied mathematics; applied partial differential equations; integral transforms; fluid dynamics; continuum mechanics; nonlinear waves; wave motions in fluids and solids
Dr. Firdous Ahmad Shah

Guest Editor
Department of Mathematics, University of Kashmir, South Campus, Anantnag, Jammu and Kashmir 192101, India

Special Issue Information

Dear Colleagues,

Wavelet transforms serve as an important and powerful computational tool for describing complex systems and analyzing empirical continuous data obtained from many kinds of signals at different scales of resolution. They have been successfullyapplied for a wide range of problems arising in physics, mathematics, and engineering, especially in signal processing, image processing, sampling theory, differential and integral equations, function spaces, quantum mechanics, neurosciences, astrophysics, computer sciences, neural networks, nanotechnology, and medicine. Over the last couple of decades, there had been a continuous research effort in the study of wavelet transforms to develop new mathematical transforms, based on wavelets, including ridgelets, curvelets, contourlets, surfacelets, flaglets, beamlets, platelets, and shearlets. In addition to these, there has been a considerable interest in the problem of constructing wavelet bases on various spaces other than R, such as abstract Hilbert spaces, locally compact Abelian groups, p-adic fields, Hyrer-groups, Lie groups, and manifolds.

The main purpose of this Special Issue is to provide a multidisciplinary forum for contributions on these new ways of constructing wavelets and the most recent advances in its applications to real world problems. This Special Issue will also be an opportunity for extending the research fields of differential and integral equations, harmonic analysis, signal and image processing, approximation theory and practical studies of Physics and Engineering. This Special Issue is expected to welcome articles of significant and original results and survey articles of exceptional merit, which are closely related to wavelet transforms in either theoretical or applicative sense.

Potential topics include, but are not limited to:

  • Continuous wavelet transforms
  • Discrete wavelet transforms
  • Fractional wavelet transforms
  • Uncertainty principles
  • Wavelet frames
  • Contineous frames
  • Shearlets
  • Wavelets on manifolds
  • Wavelets on p-adic fields
  • Wavelets on Lie groups
  • Applications

Prof. Dr. Lokenath Debnath
Dr. Firdous Ahmad Shah
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 papers will be 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. Mathematics 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 1200 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

  • Wavelet transform
  • Wavelet frame
  • Contineous frames
  • Uncertainty principle
  • Fractional wavelet
  • Ridgelet
  • Countourlet
  • Shearlet
  • Surfacelet
  • curvelets
  • Manifolds
  • Local fields
  • p-adic fields
  • Lie groups
  • LCAG groups
  • Image processing
  • Differential and integral equations
  • Deniosing, Shrinkage

Published Papers (1 paper)

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Research

Open AccessFeature PaperArticle
Wavelet Neural Network Model for Yield Spread Forecasting
Mathematics 2017, 5(4), 72; https://doi.org/10.3390/math5040072 - 27 Nov 2017
Cited by 2
Abstract
In this study, a hybrid method based on coupling discrete wavelet transforms (DWTs) and artificial neural network (ANN) for yield spread forecasting is proposed. The discrete wavelet transform (DWT) using five different wavelet families is applied to decompose the five different yield spreads [...] Read more.
In this study, a hybrid method based on coupling discrete wavelet transforms (DWTs) and artificial neural network (ANN) for yield spread forecasting is proposed. The discrete wavelet transform (DWT) using five different wavelet families is applied to decompose the five different yield spreads constructed at shorter end, longer end, and policy relevant area of the yield curve to eliminate noise from them. The wavelet coefficients are then used as inputs into Levenberg-Marquardt (LM) ANN models to forecast the predictive power of each of these spreads for output growth. We find that the yield spreads constructed at the shorter end and policy relevant areas of the yield curve have a better predictive power to forecast the output growth, whereas the yield spreads, which are constructed at the longer end of the yield curve do not seem to have predictive information for output growth. These results provide the robustness to the earlier results. Full article
(This article belongs to the Special Issue Recent Developments in Wavelet Transforms and Their Applications)
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