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Cohen–Daubechies–Feauveau Wavelet
Cohen–Daubechies–Feauveau wavelets are a family of biorthogonal wavelets that was made popular by Ingrid Daubechies. These are not the same as the orthogonal Daubechies wavelets, and also not very similar in shape and properties. However, their construction idea is the same. The JPEG 2000 compression standard uses the biorthogonal Le Gall–Tabatabai (LGT) 5/3 wavelet (developed by D. Le Gall and Ali J. Tabatabai) for lossless compression and a CDF 9/7 wavelet for lossy compression. Properties * The primal generator is a B-spline if the simple factorization q_\text(X) = 1 (see below) is chosen. * The dual generator has the highest possible number of smoothness factors for its length. * All generators and wavelets in this family are symmetric. Construction For every positive integer ''A'' there exists a unique polynomial Q_A(X) of degree ''A'' − 1 satisfying the identity :\left(1 - \frac\right)^A\,Q_A(X) + \left(\frac\right)^A\,Q_A(2 - X) = 1. This is the same polyno ... [...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] |
Primal Generator
Primal may refer to: Psychotherapy * Primal (in primal therapy), the core concept, which denotes the full reliving and cathartic release of an early traumatic experience * Primal scene (in psychoanalysis), refers to the fantasizing or witnessing by a young child of a sex act between parents Mathematics * Primal, an old mathematics term for a projective hypersurface * Primal problem, a component of the duality principle in mathematical optimization theory Entertainment * "Primal" (Eureka episode), an episode of TV series ''Eureka'' * ''Primal'' (video game), an action video game for the PlayStation 2 * ''Primal'' (TV series), a 2019 animated television series * ''Primal'' (2019 film), a 2019 film starring Nicolas Cage * Optimus Primal, a character in ''Transformers'' * ''The Lost Tribe'' (2010 film), a film whose Australian DVD was entitled ''Primal'' * ''Primal'' (2010 film), an Australian horror film directed by Josh Reed * ''Far Cry Primal'', a 2016 video game Other * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fingerprint
A fingerprint is an impression left by the friction ridges of a human finger. The recovery of partial fingerprints from a crime scene is an important method of forensic science. Moisture and grease on a finger result in fingerprints on surfaces such as glass or metal. Deliberate impressions of entire fingerprints can be obtained by ink or other substances transferred from the peaks of friction ridges on the skin to a smooth surface such as paper. Fingerprint records normally contain impressions from the pad on the last joint of fingers and thumbs, though fingerprint cards also typically record portions of lower joint areas of the fingers. Human fingerprints are detailed, unique, difficult to alter, and durable over the life of an individual, making them suitable as long-term markers of human identity. They may be employed by police or other authorities to identify individuals who wish to conceal their identity, or to identify people who are incapacitated or dead and thus unab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lifting Scheme
The lifting scheme is a technique for both designing wavelets and performing the discrete wavelet transform (DWT). In an implementation, it is often worthwhile to merge these steps and design the wavelet filters ''while'' performing the wavelet transform. This is then called the second-generation wavelet transform. The technique was introduced by Wim Sweldens. The lifting scheme factorizes any discrete wavelet transform with finite filters into a series of elementary convolution operators, so-called lifting steps, which reduces the number of arithmetic operations by nearly a factor two. Treatment of signal boundaries is also simplified. The discrete wavelet transform applies several filters separately to the same signal. In contrast to that, for the lifting scheme, the signal is divided like a zipper. Then a series of convolution–accumulate operations across the divided signals is applied. Basics The simplest version of a forward wavelet transform expressed in the lifting s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment (mathematics)
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis. For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from to ) uniquely determines the distribution ( Hausdorff moment problem). The same is not true on unbounded intervals ( Hamburger moment problem). In the mid-nineteenth century, Pafnuty Chebyshev became the first person to think systematically in terms of the moments of random variables. Significance of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet Bior2
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 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haar Wavelet
In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis. The Haar sequence is now recognised as the first known wavelet basis and is extensively used as a teaching example. The Haar sequence was proposed in 1909 by Alfréd Haar. Haar used these functions to give an example of an orthonormal system for the space of square-integrable functions on the unit interval , 1 The study of wavelets, and even the term "wavelet", did not come until much later. As a special case of the Daubechies wavelet, the Haar wavelet is also known as Db1. The Haar wavelet is also the simplest possible wavelet. The technical disadvantage of the Haar wavelet is that it is not continuous, and therefore not differentiable. This property can, however, be an advantage ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Generator
Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual number, a number system used in automatic differentiation * Dual (grammatical number), a grammatical category used in some languages * Dual county, a Gaelic games county which competes in both Gaelic football and hurling * Dual diagnosis, a psychiatric diagnosis of co-occurrence of substance abuse and a mental problem * Dual fertilization, simultaneous application of a P-type and N-type fertilizer * Dual impedance, electrical circuits that are the dual of each other * Dual SIM cellphone supporting use of two SIMs * Aerochute International Dual a two-seat Australian powered parachute design Acronyms and other uses * Dual (brand), a manufacturer of Hifi equipment * DUAL (cognitive architecture), an artificial intelligence design model * DUAL algorithm, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
B-spline
In numerical analysis, a B-spline (short for basis spline) is a type of Spline (mathematics), spline function designed to have minimal Support (mathematics), support (overlap) for a given Degree of a polynomial, degree, smoothness, and set of breakpoints (Knot (mathematics), knots that partition its Domain of a function, domain), making it a fundamental building block for all spline functions of that degree. A B-spline is defined as a piecewise polynomial of Order (mathematics), order n, meaning a degree of n - 1. It’s built from sections that meet at these knots, where the continuity of the function and its Derivative, derivatives depends on how often each knot repeats (its multiplicity). Any spline function of a specific degree can be uniquely expressed as a linear combination of B-splines of that degree over the same knots, a property that makes them versatile in mathematical modeling. A special subtype, cardinal B-splines, uses equidistant knots. The concept of B-splines tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lossy Compression
In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. Higher degrees of approximation create coarser images as more details are removed. This is opposed to lossless data compression (reversible data compression) which does not degrade the data. The amount of data reduction possible using lossy compression is much higher than using lossless techniques. Well-designed lossy compression technology often reduces file sizes significantly before degradation is noticed by the end-user. Even when noticeable by the user, further data reduction may be desirable (e.g., for real-time communication or to reduce transmission times or storage needs). The most widely used lossy compression algorithm is the discrete cosine transform (DCT), first published by N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biorthogonal Wavelet
A Biorthogonal wavelet is a wavelet where the associated wavelet transform is invertible but not necessarily orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendic .... Designing biorthogonal wavelets allows more degrees of freedom than orthogonal wavelets. One additional degree of freedom is the possibility to construct symmetric wavelet functions. In the biorthogonal case, there are two scaling functions \phi,\tilde\phi, which may generate different multiresolution analyses, and accordingly two different wavelet functions \psi,\tilde\psi. So the numbers ''M'' and ''N'' of coefficients in the scaling sequences a,\tilde a may differ. The scaling sequences must satisfy the following biorthogonality condition :\sum_ a_n \tilde a_=2\cdot\delta_. Then the wavelet sequences can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lossless Compression
Lossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates (and therefore reduced media sizes). By operation of the pigeonhole principle, no lossless compression algorithm can shrink the size of all possible data: Some data will get longer by at least one symbol or bit. Compression algorithms are usually effective for human- and machine-readable documents and cannot shrink the size of random data that contain no redundancy. Different algorithms exist that are designed either with a specific type of input data in mind or with specific assumptions about what kinds of redundancy the uncompressed data are likely to contain. Lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
