A report on Data compression

Comparison of spectrograms of audio in an uncompressed format and several lossy formats. The lossy spectrograms show bandlimiting of higher frequencies, a common technique associated with lossy audio compression.
Solidyne 922: The world's first commercial audio bit compression sound card for PC, 1990
Processing stages of a typical video encoder

Process of encoding information using fewer bits than the original representation.

- Data compression
Comparison of spectrograms of audio in an uncompressed format and several lossy formats. The lossy spectrograms show bandlimiting of higher frequencies, a common technique associated with lossy audio compression.

85 related topics with Alpha

Overall

Flowchart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" or "true" (more accurately, the number b in location B is greater than or equal to the number a in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b). Similarly, IF A > B, THEN A ← A − B. The process terminates when (the contents of) B is 0, yielding the g.c.d. in A. (Algorithm derived from Scott 2009:13; symbols and drawing style from Tausworthe 1977).

Algorithm

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Algorithm is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation.

Algorithm is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation.

Flowchart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" or "true" (more accurately, the number b in location B is greater than or equal to the number a in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b). Similarly, IF A > B, THEN A ← A − B. The process terminates when (the contents of) B is 0, yielding the g.c.d. in A. (Algorithm derived from Scott 2009:13; symbols and drawing style from Tausworthe 1977).
Ada Lovelace's diagram from "note G", the first published computer algorithm
Logical NAND algorithm implemented electronically in 7400 chip
Flowchart examples of the canonical Böhm-Jacopini structures: the SEQUENCE (rectangles descending the page), the WHILE-DO and the IF-THEN-ELSE. The three structures are made of the primitive conditional GOTO (IF test THEN GOTO step xxx, shown as diamond), the unconditional GOTO (rectangle), various assignment operators (rectangle), and HALT (rectangle). Nesting of these structures inside assignment-blocks result in complex diagrams (cf. Tausworthe 1977:100, 114).
The example-diagram of Euclid's algorithm from T.L. Heath (1908), with more detail added. Euclid does not go beyond a third measuring and gives no numerical examples. Nicomachus gives the example of 49 and 21: "I subtract the less from the greater; 28 is left; then again I subtract from this the same 21 (for this is possible); 7 is left; I subtract this from 21, 14 is left; from which I again subtract 7 (for this is possible); 7 is left, but 7 cannot be subtracted from 7." Heath comments that "The last phrase is curious, but the meaning of it is obvious enough, as also the meaning of the phrase about ending 'at one and the same number'."(Heath 1908:300).
A graphical expression of Euclid's algorithm to find the greatest common divisor for 1599 and 650.
"Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division (or a "modulus" instruction). Derived from Knuth 1973:2–4. Depending on the two numbers "Inelegant" may compute the g.c.d. in fewer steps than "Elegant".
Alan Turing's statue at Bletchley Park

Some example classes are search algorithms, sorting algorithms, merge algorithms, numerical algorithms, graph algorithms, string algorithms, computational geometric algorithms, combinatorial algorithms, medical algorithms, machine learning, cryptography, data compression algorithms and parsing techniques.

The simplest way to quantize a signal is to choose the digital amplitude value closest to the original analog amplitude. This example shows the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal (yellow) and the difference between the original signal and the reconstructed signal (red). The difference between the original signal and the reconstructed signal is the quantization error and, in this simple quantization scheme, is a deterministic function of the input signal.

Quantization (signal processing)

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Process of mapping input values from a large set to output values in a (countable) smaller set, often with a finite number of elements.

Process of mapping input values from a large set to output values in a (countable) smaller set, often with a finite number of elements.

The simplest way to quantize a signal is to choose the digital amplitude value closest to the original analog amplitude. This example shows the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal (yellow) and the difference between the original signal and the reconstructed signal (red). The difference between the original signal and the reconstructed signal is the quantization error and, in this simple quantization scheme, is a deterministic function of the input signal.
2-bit resolution with four levels of quantization compared to analog.
3-bit resolution with eight levels.
Comparison of quantizing a sinusoid to 64 levels (6 bits) and 256 levels (8 bits). The additive noise created by 6-bit quantization is 12 dB greater than the noise created by 8-bit quantization. When the spectral distribution is flat, as in this example, the 12 dB difference manifests as a measurable difference in the noise floors.

Rate–distortion optimized quantization is encountered in source coding for lossy data compression algorithms, where the purpose is to manage distortion within the limits of the bit rate supported by a communication channel or storage medium.

Motion JPEG 2000

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File format for motion sequences of JPEG 2000 images and associated audio, based on the MP4 and QuickTime format.

File format for motion sequences of JPEG 2000 images and associated audio, based on the MP4 and QuickTime format.

In contrast to the original 1992 JPEG standard, which is a discrete cosine transform (DCT) based lossy compression format for static digital images, JPEG 2000 is a discrete wavelet transform (DWT) based compression standard that could be adapted for motion imaging video compression with the Motion JPEG 2000 extension.

Delta encoding

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Way of storing or transmitting data in the form of differences between sequential data rather than complete files; more generally this is known as data differencing.

Way of storing or transmitting data in the form of differences between sequential data rather than complete files; more generally this is known as data differencing.

However, in video compression, delta frames can considerably reduce frame size and are used in virtually every video compression codec.

Data differencing

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Producing a technical description of the difference between two sets of data – a source and a target.

Producing a technical description of the difference between two sets of data – a source and a target.

Data compression can be seen as a special case of data differencing – data differencing consists of producing a difference given a source and a target, with patching producing a target given a source and a difference, while data compression consists of producing a compressed file given a target, and decompression consists of producing a target given only a compressed file.

CABAC method of entropy encoding used within H264 video compression standard in English

Context-adaptive binary arithmetic coding

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Form of entropy encoding used in the H.264/MPEG-4 AVC and High Efficiency Video Coding (HEVC) standards.

Form of entropy encoding used in the H.264/MPEG-4 AVC and High Efficiency Video Coding (HEVC) standards.

CABAC method of entropy encoding used within H264 video compression standard in English

CABAC is notable for providing much better compression than most other entropy encoding algorithms used in video encoding, and it is one of the key elements that provides the H.264/AVC encoding scheme with better compression capability than its predecessors.

Trade-off

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Situational decision that involves diminishing or losing one quality, quantity, or property of a set or design in return for gains in other aspects.

Situational decision that involves diminishing or losing one quality, quantity, or property of a set or design in return for gains in other aspects.

By compressing an image, you can reduce transmission time/costs at the expense of CPU time to perform the compression and decompression. Depending on the compression method, this may also involve the tradeoff of a loss in image quality.

The product of a Boolean function and a Walsh matrix is its Walsh spectrum: (1, 0, 1, 0, 0, 1, 1, 0) × H(8) = (4, 2, 0, −2, 0, 2, 0, 2)

Hadamard transform

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Example of a generalized class of Fourier transforms.

Example of a generalized class of Fourier transforms.

The product of a Boolean function and a Walsh matrix is its Walsh spectrum: (1, 0, 1, 0, 0, 1, 1, 0) × H(8) = (4, 2, 0, −2, 0, 2, 0, 2)
Fast Walsh–Hadamard transform, a faster way to calculate the Walsh spectrum of (1, 0, 1, 0, 0, 1, 1, 0).
The original function can be expressed by means of its Walsh spectrum as an arithmetical polynomial.

The Hadamard transform is also used in data encryption, as well as many signal processing and data compression algorithms, such as JPEG XR and MPEG-4 AVC.

Illustration of the relative entropy for two normal distributions. The typical asymmetry is clearly visible.

Kullback–Leibler divergence

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Type of statistical distance: a measure of how one probability distribution P is different from a second, reference probability distribution Q.

Type of statistical distance: a measure of how one probability distribution P is different from a second, reference probability distribution Q.

Illustration of the relative entropy for two normal distributions. The typical asymmetry is clearly visible.

Just as absolute entropy serves as theoretical background for data compression, relative entropy serves as theoretical background for data differencing – the absolute entropy of a set of data in this sense being the data required to reconstruct it (minimum compressed size), while the relative entropy of a target set of data, given a source set of data, is the data required to reconstruct the target given the source (minimum size of a patch).

Microphone covers are occasionally used to improve sound quality by reducing noise from wind.

Sound quality

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Typically an assessment of the accuracy, fidelity, or intelligibility of audio output from an electronic device.

Typically an assessment of the accuracy, fidelity, or intelligibility of audio output from an electronic device.

Microphone covers are occasionally used to improve sound quality by reducing noise from wind.

However, this space can be greatly reduced using audio compression.