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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] |
Second Generation Wavelet Transform
{{Short description, Type of wavelet transform In signal processing, the second-generation wavelet transform (SGWT) is a wavelet transform where the filters (or even the represented wavelets) are not designed explicitly, but the transform consists of the application of the Lifting scheme. Actually, the sequence of lifting steps could be converted to a regular discrete wavelet transform, but this is unnecessary because both design and application is made via the lifting scheme. This means that they are not designed in the frequency domain, as they are usually in the ''classical'' (so to speak ''first generation'') transforms such as the DWT and CWT). The idea of moving away from the Fourier domain was introduced independently by David Donoho and Harten in the early 1990s. Calculating transform The input signal f is split into odd \gamma _1 and even \lambda _1 samples using shifting and downsampling. The detail coefficients \gamma _2 are then interpolated using the values of \ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Signal Processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent Sampling (signal processing), samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor. Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include Audio signal processing, audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feistel Scheme
In cryptography, a Feistel cipher (also known as Luby–Rackoff block cipher) is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel, who did pioneering research while working for IBM; it is also commonly known as a Feistel network. A large number of block ciphers use the scheme, including the US Data Encryption Standard, the Soviet/Russian GOST and the more recent Blowfish and Twofish ciphers. In a Feistel cipher, encryption and decryption are very similar operations, and both consist of iteratively running a function called a " round function" a fixed number of times. History Many modern symmetric block ciphers are based on Feistel networks. Feistel networks were first seen commercially in IBM's Lucifer cipher, designed by Horst Feistel and Don Coppersmith in 1973. Feistel networks gained respectability when the U.S. Federal Government adopted the DES (a cipher based on Lucifer, with changes mad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-separable Wavelet
Non-separable wavelets are multi-dimensional wavelets that are not directly implemented as tensor products of wavelets on some lower-dimensional space. They have been studied since 1992. They offer a few important advantages. Notably, using non-separable filters leads to more parameters in design, and consequently better filters. The main difference, when compared to the one-dimensional wavelets, is that multi-dimensional sampling requires the use of lattices (e.g., the quincunx lattice). The wavelet filters themselves can be separable or non-separable regardless of the sampling lattice. Thus, in some cases, the non-separable wavelets can be implemented in a separable fashion. Unlike separable wavelet, the non-separable wavelets are capable of detecting structures that are not only horizontal, vertical or diagonal (show less anisotropy). Examples * Red-black wavelets * Contourlets * Shearlet In applied mathematical analysis, shearlets are a multiscale framework which allows effi ... [...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] |
Image Compression
Image compression is a type of data compression applied to digital images, to reduce their cost for computer data storage, storage or data transmission, transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data. Lossy and lossless image compression Image compression may be lossy compression, lossy or lossless compression, lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics. Lossy compression methods, especially when used at low bit rates, introduce compression artifacts. Lossy methods are especially suitable for natural images such as photographs in applications where minor (sometimes imperceptible) loss of fidelity is acceptable to achieve a substantial reduction in bit rate. Lossy compression that produces negligible differences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set. A function is bijective if it is invertible; that is, a function f:X\to Y is bijective if and only if there is a function g:Y\to X, the ''inverse'' of , such that each of the two ways for composing the two functions produces an identity function: g(f(x)) = x for each x in X and f(g(y)) = y for each y in Y. For example, the ''multiplication by two'' defines a bijection from the integers to the even numbers, which has the ''division by two'' as its inverse function. A function is bijective if and only if it is both injective (or ''one-to-one'')—meaning that each element in the codomain is mappe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Injective Function
In mathematics, an injective function (also known as injection, or one-to-one function ) is a function that maps distinct elements of its domain to distinct elements of its codomain; that is, implies (equivalently by contraposition, implies ). In other words, every element of the function's codomain is the image of one element of its domain. The term must not be confused with that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain. A homomorphism between algebraic structures is a function that is compatible with the operations of the structures. For all common algebraic structures, and, in particular for vector spaces, an is also called a . However, in the more general context of category theory, the definition of a monomorphism differs from that of an injective homomorphism. This is thus a theorem that they are equivalent for algebraic structures; see for more details. A func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map (mathematics)
In mathematics, a map or mapping is a function (mathematics), function in its general sense. These terms may have originated as from the process of making a map, geographical map: ''mapping'' the Earth surface to a sheet of paper. The term ''map'' may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term ''transformation'' can be used interchangeably, but ''transformation (function), transformation'' often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory. Maps as functions In many branches of mathematics, the term ''map'' is used to mean a Function (mathematics), function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a "continuous f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interleaving (data)
In computing, interleaving of data refers to the interspersing of fields or channels of different meaning sequentially in memory, in processor registers, or in file formats. For example, for coordinate data, :x0 y0 z0 w0 x1 y1 z1 w1 x2 y2 z2 w2 :x0 x1 x2 x3 y0 y1 y2 y3 z0 z1 z2 z3 w0 w1 w2 w3 the former is interleaved while the latter is not. A processor may support permute instructions, or strided load and store instructions, for moving between interleaved and non-interleaved representations. Interleaving has performance implications for cache coherency, ease of leveraging SIMD hardware, and leveraging a computer's addressing modes. (e.g. - interleaved data may require one address to be calculated, from which individual fields may then be accessed via immediate offsets; conversely if only one field is required by index, de-interleaved data may leverage scaled index addressing). See also * AOS vs SOA * Data-oriented design * Locality of reference * Parallel array In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Receiver (information Theory)
The receiver in information theory is the receiving end of a communication channel. It receives decoded messages/information from the sender, who first encoded them. Sometimes the receiver is modeled so as to include the decoder. Real-world receivers like radio receivers or telephones can not be expected to receive as much information as predicted by the noisy channel coding theorem. Real-world receivers include: * For modulated radio waves, a radio receiver ** For converting specifically AM modulated radio waves to sound, an AM Tuner ** For converting specifically FM modulated radio waves to sound, an FM Tuner ** For converting specifically television transmissions to video and audio, a television tuner, which may be a component of an AV receiver * For modulated ultrasound waves, a receiver (modulated ultrasound) * For converting analog electrical signals on a wire to audio, a speaker system, which may be a component of an audio headset or telephone handset. * For readin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
