A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing.
The Daubechies wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support. With each wavelet type of this class, there is a scaling function which generates an orthogonal multiresolution analysis.
Stéphane Georges Mallat is a French applied mathematician, concurrently appointed as Professor at Collège de France and École normale supérieure. He made fundamental contributions to the development of wavelet theory in the late 1980s and early 1990s. He has additionally done work in applied mathematics, signal processing, music synthesis and image segmentation.
Baroness Ingrid Daubechies is a Belgian-American physicist and mathematician. She is best known for her work with wavelets in image compression.
In numerical analysis, a multigrid method is an algorithm for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in problems exhibiting multiple scales of behavior. For example, many basic relaxation methods exhibit different rates of convergence for short- and long-wavelength components, suggesting these different scales be treated differently, as in a Fourier analysis approach to multigrid. MG methods can be used as solvers as well as preconditioners.
Yves F. Meyer is a French mathematician. He is among the progenitors of wavelet theory, having proposed the Meyer wavelet. Meyer was awarded the Abel Prize in 2017.
In mathematics, a wavelet series is a representation of a square-integrable function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform.
Ali Naci Akansu is a Turkish-American professor of electrical & computer engineering and scientist in applied mathematics.
Inverse Problems is a peer-reviewed, broad-based interdisciplinary journal for pure and applied mathematicians and physicists produced by IOP Publishing. It combines theoretical, experimental and mathematical papers on inverse problems with numerical and practical approaches to their solution. The journal has a specialized relevance to workers in geophysics, optics, radar, acoustics, communication theory, signal processing and medical imaging.
Multiscale geometric analysis or geometric multiscale analysis is an emerging area of high-dimensional signal processing and data analysis.
Scientia Iranica is a peer-reviewed scientific journal published by Sharif University of Technology. It was established in 1991 and covers theoretical and experimental research in technical sciences and engineering. Starting in 2011, the journal is published open access. The editor-in-chief is Abolhassan Vafai.
Algorithmica is a monthly peer-reviewed scientific journal focusing on research and the application of computer science algorithms. The journal was established in 1986 and is published by Springer Science+Business Media. The editor in chief is Mohammad Hajiaghayi. Subject coverage includes sorting, searching, data structures, computational geometry, and linear programming, VLSI, distributed computing, parallel processing, computer aided design, robotics, graphics, data base design, and software tools.
The Journal of Software: Evolution and Process is a peer-reviewed scientific journal covering all aspects of software development and evolution. It is published by John Wiley & Sons. The journal was established in 1989 as the Journal of Software Maintenance: Research and Practice, renamed in 2001 to Journal of Software Maintenance and Evolution: Research and Practice, and obtained its current title in 2012. The editors-in-chief are Massimiliano Di Penta, Darren Dalcher, Xin Peng, and David Raffo.
The International Journal of Computational Geometry and Applications (IJCGA) is a bimonthly journal published since 1991, by World Scientific. It covers the application of computational geometry in design and analysis of algorithms, focusing on problems arising in various fields of science and engineering such as computer-aided geometry design (CAGD), operations research, and others.
Open Systems & Information Dynamics (OSID) is a journal published by World Scientific. It covers interdisciplinary research in mathematics, physics, engineering and life sciences based upon the fields of information processing, storage and transmission, in both quantum and classical settings, with a theoretical focus. Topics include quantum information theory, open systems, decoherence, complexity theory of classical and quantum systems and other models of information processing.
Annals of Science is a peer-reviewed academic journal covering the history of science and technology. It is published by Taylor & Francis and was established in 1936. The founding editor-in-chief was the Canadian historian of science Harcourt Brown.
Cybernetics and Systems is a peer-reviewed scientific journal of cybernetics and systems science, including artificial intelligence, computer science, cybernetics, human computer intelligence, information and communication technology, machine learning, and robotics. The journal was established in 1971 as Journal of Cybernetics and obtained its current title in 1980. It is published by Taylor & Francis in cooperation with the Austrian Society for Cybernetic Studies and the editor-in-chief is Robert Trappl.
Information Systems is a peer-reviewed scientific journal covering data-intensive technologies underlying database systems, business processes, social media, and data science. It is published 8 times a year by Elsevier. The editors-in-chief are Dennis Shasha, Gottfried Vossen, and Matthias Weidlich.
Radovan Stojanović is the Professor of Electrical Engineering at the University of Montenegro, Montenegro and Founder and President of the Montenegrin Association for New Technologies (MANT). He is a member of the Board of the Montenegrin Academy of Sciences and Arts for Natural and Technical Sciences.
Multiresolution Fourier Transform is an integral fourier transform that represents a specific wavelet-like transform with a fully scalable modulated window, but not all possible translations.
