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Image compression is a type of data compression applied to digital images, to reduce their cost for storage or 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.
The Hadamard transform H m is a 2 m × 2 m matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2 m real numbers x n into 2 m real numbers X k.The Hadamard transform can be defined in two ways: recursively, or by using the binary (base-2) representation of the indices n and k.
The sum of absolute transformed differences (SATD) is a block matching criterion widely used in fractional motion estimation for video compression.It works by taking a frequency transform, usually a Hadamard transform, of the differences between the pixels in the original block and the corresponding pixels in the block being used for comparison.
Discrete sine transform; Discrete wavelet transform; Hadamard transform (or, Walsh–Hadamard transform) Fast wavelet transform; Hankel transform, the determinant of the Hankel matrix; Discrete Chebyshev transform. Equivalent, up to a diagonal scaling, to a discrete cosine transform; Finite Legendre transform; Spherical Harmonic transform
In computational mathematics, the Hadamard ordered fast Walsh–Hadamard transform (FWHT h) is an efficient algorithm to compute the Walsh–Hadamard transform (WHT). A naive implementation of the WHT of order n = 2 m {\displaystyle n=2^{m}} would have a computational complexity of O( n 2 {\displaystyle n^{2}} ) .
Transform coding dates back to the late 1960s, with the introduction of fast Fourier transform (FFT) coding in 1968 and the Hadamard transform in 1969. [34] An important image compression technique is the discrete cosine transform (DCT), a technique developed in the early 1970s. [16]
Applications of the Walsh functions can be found wherever digit representations are used, including speech recognition, medical and biological image processing, and digital holography. For example, the fast Walsh–Hadamard transform (FWHT) may be used in the analysis of digital quasi-Monte Carlo methods.
CCITT Group 4 compression, also referred to as G4 or Modified Modified READ (MMR), is a lossless method of image compression used in Group 4 fax machines defined in the ITU-T T.6 fax standard. It is only used for bitonal (black-and-white) images.