Special Issue "Wavelets and Applications"
A special issue of Axioms (ISSN 2075-1680).
Deadline for manuscript submissions: closed (15 April 2013)
Prof. Dr. Palle Jorgensen
Department of Mathematics, 14 MLH, The University of Iowa, Iowa City, IA 52242-1419, USA
Phone: +1 319 335 0782
Interests: mathematical analysis including harmonic analysis; functional analysis; operator theory and operator algebras; mathematical physics; representation theory; wavelets
Recently, there has been an enormous amount of interest in the theory and applications of wavelets. The applications include signal processing, data compression, turning fingerprints into digital data files, subdivision algorithms for graphics, and the JPEG 2000 encoding of images. As a mathematical subject, wavelet theory involves tools from a host of neighboring fields, functional and harmonic analysis, numerical analysis, mathematics of computation, and operator theory.
Wavelets now serve as an alternative to classical Fourier methods, Fourier series and integrals. The reasons for this is that they are better localized, they are better adapted to discontinuities; they have a certain
form of self-similarity, which makes the theory suited for the analysis of fractals and non-linear dynamical systems. The self-similarity properties of the scaling functions connect them to fractals and non-linear dynamical systems.
The multiresolutions offer fast algorithms. The feature of localization for wavelets is shared by related recursive basis constructions from multi-resolutions in Hilbert spaces, for example for fractals and iterated function systems in dynamics. The multiresolutions and locality yield much better pointwise approximations than is possible for traditional Fourier bases.
In signal or image-processing one is interested in subdividing analogue-signals into frequency bands. This idea goes back to Norbert Wiener, but it is of relevance in modern-day wireless signal and image processing. This suggests a representation theoretic framework. The idea is thus to build a representation theory which creates Hilbert spaces H and specific families of closed subspaces in H in such a way that "non-overlapping frequency bands" in our model correspond to orthogonal subspaces in H; or equivalently to systems of orthogonal projections. Since the different frequency bands must exhaust the signals for the entire system, one looks for orthogonal projections which add to the identity operator in H. Since time/frequency analysis is non-commutative, one is further faced with a selection of special families of commuting orthogonal projections. When an iteration scheme is applied to the initial generators, one generates new bases and frames by repeated subdivision sequences; wavelet families as recursive scheme.
Professor Palle Jorgensen
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. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as 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 refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed Open Access quarterly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. For the first couple of issues the Article Processing Charge (APC) will be waived for well-prepared manuscripts. English correction and/or formatting fees of 250 CHF (Swiss Francs) will be charged in certain cases for those articles accepted for publication that require extensive additional formatting and/or English corrections.
- applied harmonic analysis
- signal and image processing
- fourier methods
- operators in Hilbert space
- wavelet filters
- filter bank
Axioms 2013, 2(3), 311-344; doi:10.3390/axioms2030311
Received: 7 April 2013; in revised form: 15 May 2013 / Accepted: 4 June 2013 / Published: 9 July 2013| PDF Full-text (563 KB)
Axioms 2013, 2(3), 345-370; doi:10.3390/axioms2030345
Received: 5 June 2013; in revised form: 18 June 2013 / Accepted: 19 June 2013 / Published: 9 July 2013| PDF Full-text (1348 KB)
Axioms 2013, 2(3), 371-389; doi:10.3390/axioms2030371
Received: 17 April 2013; in revised form: 28 June 2013 / Accepted: 1 July 2013 / Published: 9 July 2013| PDF Full-text (952 KB)
Article: Some Notes on the Use of the Windowed Fourier Transform for Spectral Analysis of Discretely Sampled Data
Axioms 2013, 2(3), 286-310; doi:10.3390/axioms2030286
Received: 24 April 2013; in revised form: 20 May 2013 / Accepted: 21 May 2013 / Published: 24 June 2013| PDF Full-text (882 KB)
Axioms 2013, 2(2), 271-285; doi:10.3390/axioms2020271
Received: 24 April 2013; in revised form: 17 May 2013 / Accepted: 22 May 2013 / Published: 18 June 2013| Cited by 1 | PDF Full-text (607 KB) | Supplementary Files
Article: Quantitative Hahn-Banach Theorems and Isometric Extensions for Wavelet and Other Banach Spaces
Axioms 2013, 2(2), 224-270; doi:10.3390/axioms2020224
Received: 4 March 2013; in revised form: 12 May 2013 / Accepted: 14 May 2013 / Published: 23 May 2013| PDF Full-text (431 KB)
Article: A Sequential, Implicit, Wavelet-Based Solver for Multi-Scale Time-Dependent Partial Differential Equations
Axioms 2013, 2(2), 142-181; doi:10.3390/axioms2020142
Received: 28 February 2013; Accepted: 8 April 2013 / Published: 23 April 2013| PDF Full-text (907 KB)
Axioms 2013, 2(2), 182-207; doi:10.3390/axioms2020182
Received: 16 February 2013; in revised form: 18 March 2013 / Accepted: 28 March 2013 / Published: 23 April 2013| PDF Full-text (1336 KB)
Axioms 2013, 2(2), 122-141; doi:10.3390/axioms2020122
Received: 5 February 2013; in revised form: 21 March 2013 / Accepted: 26 March 2013 / Published: 17 April 2013| PDF Full-text (260 KB)
Axioms 2013, 2(2), 100-121; doi:10.3390/axioms2020100
Received: 24 December 2012; in revised form: 16 March 2013 / Accepted: 18 March 2013 / Published: 11 April 2013| Cited by 1 | PDF Full-text (528 KB)
Article: Mollification Based on Wavelets
Axioms 2013, 2(2), 67-84; doi:10.3390/axioms2020067
Received: 9 January 2013; in revised form: 11 March 2013 / Accepted: 19 March 2013 / Published: 25 March 2013| PDF Full-text (626 KB)
Article: Signal Estimation Using Wavelet Analysis of Solution Monitoring Data for Nuclear Safeguards
Axioms 2013, 2(1), 44-57; doi:10.3390/axioms2010044
Received: 31 January 2013; in revised form: 4 March 2013 / Accepted: 7 March 2013 / Published: 20 March 2013| PDF Full-text (499 KB)
Last update: 18 February 2013