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Discrete Wavelet Transform
In numerical analysis and functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ..., a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency ''and'' location information (location in time). Definition One level of the transform The DWT of a signal x is calculated by passing it through a series of filters. First the samples are passed through a low-pass filter with impulse response g resulting in a convolution of the two: :y[n] = (x * g)[n] = \sum\limits_^\infty The signal is also decomposed simultaneously using a high-pass filter h. The outputs give the detail coefficients (fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jpeg2000 2-level Wavelet Transform-lichtenstein
JPEG ( , short for Joint Photographic Experts Group and sometimes retroactively referred to as JPEG 1) is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography. The degree of compression can be adjusted, allowing a selectable trade off between storage size and image quality. JPEG typically achieves 10:1 compression with noticeable, but widely agreed to be acceptable perceptible loss in image quality. Since its introduction in 1992, JPEG has been the most widely used image compression standard in the world, and the most widely used digital image format, with several billion JPEG images produced every day as of 2015. The Joint Photographic Experts Group created the standard in 1992, based on the discrete cosine transform (DCT) algorithm. JPEG was largely responsible for the proliferation of digital images and digital photos across the Internet and later social media. JPEG compression is used in a number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet
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. For example, a wavelet could be created to have a frequency of middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications. As a mathematical tool, wavelets can be used to extract information from many kinds of data, including audio signals and images. Sets of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal completed the next year, after a regulatory review. Thus, Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ... Well-known products include the '' Methods in Enzymology'' series and encyclopedias such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ITU-T
The International Telecommunication Union Telecommunication Standardization Sector (ITU-T) is one of the three Sectors (branches) of the International Telecommunication Union (ITU). It is responsible for coordinating Standardization, standards for telecommunications and Information Communication Technology, such as X.509 for cybersecurity, Y.3172 and Y.3173 for machine learning, and H.264/MPEG-4 AVC for video compression, between its Member States, Private Sector Members, and Academia Members. The World Telecommunication Standardization Assembly (WTSA), the sector's governing conference, convenes every four years. ITU-T has a permanent Secretariat (administrative office), secretariat called the Telecommunication Standardization Bureau (TSB), which is based at the ITU headquarters in Geneva, Switzerland. The current director of the TSB is Seizo Onoe (of Japan), whose 4-year term commenced on 1 January 2023. Seizo Onoe succeeded Chaesub Lee of South Korea, who was director from 1 J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Video Coding Experts Group
The Video Coding Experts Group or Visual Coding Experts Group (VCEG, also known as Question 6) is a working group of the ITU Telecommunication Standardization Sector (ITU-T) concerned with standards for compression coding of video, images, audio signals, biomedical waveforms, and other signals. It is responsible for standardization of the "H.26x" line of video coding standards, the "T.8xx" line of image coding standards, and related technologies. Administratively, VCEG is the informal name of Question 6 (Visual, audio and signal coding) of Working Party 3 (Audiovisual technologies and intelligent immersive applications) of ITU-T Study Group 16 (Multimedia and related digital technologies). Its abbreviated title is ITU-T Q.6/SG16, or more simply, ITU-T Q6/16. The goal of VCEG is to produce ITU-T Recommendations (international standards) for video coding and image coding methods appropriate for conversational (e.g. videoconferencing and video telephony) and non-conversational (e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JPEG XS
JPEG XS (standardized as ISO/IEC 21122) is an image and video codec that offers visually and mathematically lossless quality. It is a special-purpose codec that is specifically designed to allow for low-complexity and low-latency implementations. Target applications of the standard include streaming high-quality content for professional video over IP (SMPTE ST 2022 and ST 2110) in broadcast and other applications, virtual reality, drones, autonomous vehicles using cameras, gaming. Although there is not an official acronym definition, XS was chosen to highlight the ''extra small'' and ''extra speed'' characteristics of the codec. Features Three main features are key to JPEG XS: # Visually transparent compression: XS compressed content is indistinguishable from the original uncompressed content (passing ISO/IEC 29170-2 tests, also called AIC-2) for compression ratios between 2:1 and 10:1. # Low latency: The total end-to-end latency, introduced by the JPEG XS compression-decom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JPEG 2000
JPEG 2000 (JP2) is an image compression standard and coding system. It was developed from 1997 to 2000 by a Joint Photographic Experts Group committee chaired by Touradj Ebrahimi (later the JPEG president), with the intention of superseding their original JPEG standard (created in 1992), which is based on a discrete cosine transform (DCT), with a newly designed, wavelet-based method. The standardized filename extension is .jp2 for International Organization for Standardization, ISO/International Electrotechnical Commission, IEC 15444-1 conforming files and .jpx for the extended part-2 specifications, published as ISO/IEC 15444-2. The Internet media type, MIME types for JPEG 2000 are defined in RFC 3745. The MIME type for JPEG 2000 (ISO/IEC 15444-1) is image/jp2. The JPEG 2000 project was motivated by Ricoh, Ricoh's submission in 1995 of the CREW (Compression with Reversible Embedded Wavelets) algorithm to the standardization effort of JPEG LS. Ultimately the Lossless JPEG#LOCO-I_a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daubechies Wavelet
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 (called the ''father wavelet'') which generates an orthogonal multiresolution analysis. Properties In general the Daubechies wavelets are chosen to have the highest number ''A'' of vanishing moments, (this does not imply the best smoothness) for given support width (number of coefficients) 2''A''. There are two naming schemes in use, D''N'' using the length or number of taps, and db''A'' referring to the number of vanishing moments. So D4 and db2 are the same wavelet transform. Among the 2''A''−1 possible solutions of the algebraic equations for the moment and orthogonality conditions, the one is chosen whose scaling filter has extremal phase. The wavelet transform is also easy to put int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ingrid Daubechies
Baroness Ingrid Daubechies ( ; ; born 17 August 1954) is a Belgian-American physicist and mathematician. She is best known for her work with wavelets in image compression. Daubechies is recognized for her study of the mathematical methods that enhance image-compression technology. She is a member of the National Academy of Engineering, the National Academy of Sciences and the American Academy of Arts and Sciences. She is a 1992 MacArthur Fellow. She also served on the Mathematical Sciences jury for the Infosys Prize from 2011 to 2013. The name Daubechies is widely associated with the orthogonal Daubechies wavelet and the biorthogonal CDF wavelet. A wavelet from this family of wavelets is now used in the JPEG 2000 standard. Her research involves the use of automatic methods from both mathematics, technology, and biology to extract information from samples such as bones and teeth. She also developed sophisticated image processing techniques used to help establish the authenti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfréd Haar
Alfréd Haar (; 11 October 1885, Budapest – 16 March 1933, Szeged) was a Kingdom of Hungary, Hungarian mathematician. In 1904 he began to study at the University of Göttingen. His doctorate was supervised by David Hilbert. The Haar measure, Haar wavelet, and Haar transform are named in his honor. Between 1912 and 1919 he taught at Franz Joseph University in Cluj-Napoca, Kolozsvár. Together with Frigyes Riesz, he made the University of Szeged a centre of mathematics. He also founded the ''Acta Scientiarum Mathematicarum'' journal together with Riesz. Biography Haar was born to a Hungarian-Jewish''Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture'', Birgit Bergmann, (Springer 2012), page 63 family in Budapest on 11 October 1885 to parents Ignác Haar and Emma Fuchs. He graduated in 1903 from the secondary school Fasori Gimnázium, Fasori Evangélikus Gimnázium where he was a student of László Rátz. He started his university studies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Series
In mathematics, a geometric series is a series (mathematics), series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant. For example, 1/2 + 1/4 + 1/8 + 1/16 + ⋯, the series \tfrac12 + \tfrac14 + \tfrac18 + \cdots is a geometric series with common ratio , which converges to the sum of . Each term in a geometric series is the geometric mean of the term before it and the term after it, in the same way that each term of an arithmetic series is the arithmetic mean of its neighbors. While Ancient Greek philosophy, Greek philosopher Zeno's paradoxes about time and motion (5th century BCE) have been interpreted as involving geometric series, such series were formally studied and applied a century or two later by Greek mathematics, Greek mathematicians, for example used by Archimedes to Quadrature of the Parabola, calculate the area inside a parabola (3rd century BCE). Today, geometric series are used in mathematical finance, calculati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrence Relation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
