Data compression

In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use.

Compression is useful because it helps reduce the consumption of expensive resources, such as hard disk space or transmission bandwidth. On the downside, compressed data must be decompressed to be used, and this extra processing may be detrimental to some applications. For instance, a compression scheme for video may require expensive hardware for the video to be decompressed fast enough to be viewed as it is being decompressed (the option of decompressing the video in full before watching it may be inconvenient, and requires storage space for the decompressed video). The design of data compression schemes therefore involves trade-offs among various factors, including the degree of compression, the amount of distortion introduced (if using a lossy compression scheme), and the computational resources required to compress and uncompress the data. Compression was one of the main drivers for the growth of information during the past two decades[1].

Contents

Lossless versus lossy compression

Lossless compression algorithms usually exploit statistical redundancy in such a way as to represent the sender's data more concisely without error. Lossless compression is possible because most real-world data has statistical redundancy. For example, in English text, the letter 'e' is much more common than the letter 'z', and the probability that the letter 'q' will be followed by the letter 'z' is very small. Another kind of compression, called lossy data compression or perceptual coding, is possible if some loss of fidelity is acceptable. Generally, a lossy data compression will be guided by research on how people perceive the data in question. For example, the human eye is more sensitive to subtle variations in luminance than it is to variations in color. JPEG image compression works in part by "rounding off" some of this less-important information. Lossy data compression provides a way to obtain the best fidelity for a given amount of compression.

Lossy

Lossy image compression is used in digital cameras, to increase storage capacities with minimal degradation of picture quality. Similarly, DVDs use the lossy MPEG-2 Video codec for video compression.

In lossy audio compression, methods of psychoacoustics are used to remove non-audible (or less audible) components of the signal. Compression of human speech is often performed with even more specialized techniques, so that "speech compression" or "voice coding" is sometimes distinguished as a separate discipline from "audio compression". Different audio and speech compression standards are listed under audio codecs. Voice compression is used in Internet telephony for example, while audio compression is used for CD ripping and is decoded by audio players.

Lossless

The Lempel–Ziv (LZ) compression methods are among the most popular algorithms for lossless storage. DEFLATE is a variation on LZ which is optimized for decompression speed and compression ratio, but compression can be slow. DEFLATE is used in PKZIP, gzip and PNG. LZW (Lempel–Ziv–Welch) is used in GIF images. Also noteworthy are the LZR (LZ–Renau) methods, which serve as the basis of the Zip method. LZ methods utilize a table-based compression model where table entries are substituted for repeated strings of data. For most LZ methods, this table is generated dynamically from earlier data in the input. The table itself is often Huffman encoded (e.g. SHRI, LZX). A current LZ-based coding scheme that performs well is LZX, used in Microsoft's CAB format.

The very best modern lossless compressors use probabilistic models, such as prediction by partial matching. The Burrows–Wheeler transform can also be viewed as an indirect form of statistical modelling.

In a further refinement of these techniques, statistical predictions can be coupled to an algorithm called arithmetic coding. Arithmetic coding, invented by Jorma Rissanen, and turned into a practical method by Witten, Neal, and Cleary, achieves superior compression to the better-known Huffman algorithm, and lends itself especially well to adaptive data compression tasks where the predictions are strongly context-dependent. Arithmetic coding is used in the bilevel image-compression standard JBIG, and the document-compression standard DjVu. The text entry system, Dasher, is an inverse-arithmetic-coder.

Theory

The theoretical background of compression is provided by information theory (which is closely related to algorithmic information theory) for lossless compression, and by rate–distortion theory for lossy compression. These fields of study were essentially created by Claude Shannon, who published fundamental papers on the topic in the late 1940s and early 1950s. Coding theory is also related. The idea of data compression is deeply connected with statistical inference.

Machine learning

There is a close connection between machine learning and compression: a system that predicts the posterior probabilities of a sequence given its entire history can be used for optimal data compression (by using arithmetic coding on the output distribution), while an optimal compressor can be used for prediction (by finding the symbol that compresses best, given the previous history). This equivalence has been used as justification for data compression as a benchmark for "general intelligence".[2]

Data differencing

Data compression can be viewed as a special case of data differencing:[3][4] 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. Thus, one can consider data compression as data differencing with empty source data, the compressed file corresponding to a "difference from nothing". This is the same as considering absolute entropy (corresponding to data compression) as a special case of relative entropy (corresponding to data differencing) with no initial data.

When one wishes to emphasize the connection, one may use the term differential compression to refer to data differencing.

Outlook and currently unused potential

It is estimated that the total amount of the information that is stored on the world's storage devices could be furthermore compressed by a remaining average factor of 4.5 : 1 with existing compression algorithms, which means that thanks to compression, the world could store 4.5 times more information on its existing storage devices than it currently does (it is estimated that the combined technological capacity of the world to store information provides 1,300 exabytes of hardware digits in 2007, but when the corresponding content is optimally compressed, this only represents 295 exabytes of Shannon information)[1].

Uses

Audio

Audio compression is a form of data compression designed to reduce the transmission bandwidth requirement of digital audio streams and the storage size of audio files. Audio compression algorithms are implemented in computer software as audio codecs. Generic data compression algorithms perform poorly with audio data, seldom reducing data size much below 87% from the original,[citation needed] and are not designed for use in real time applications. Consequently, specifically optimized audio lossless and lossy algorithms have been created. Lossy algorithms provide greater compression rates and are used in mainstream consumer audio devices.

In both lossy and lossless compression, information redundancy is reduced, using methods such as coding, pattern recognition and linear prediction to reduce the amount of information used to represent the uncompressed data.

The trade-off between slightly reduced audio quality and transmission or storage size is outweighed by the latter for most practical audio applications in which users may not perceive the loss in playback rendition quality. For example, one Compact Disc holds approximately one hour of uncompressed high fidelity music, less than 2 hours of music compressed losslessly, or 7 hours of music compressed in the MP3 format at medium bit rates.

Lossless audio compression

Lossless audio compression produces a representation of digital data that can be expanded to an exact digital duplicate of the original audio stream. This is in contrast to the irreversible changes upon playback from lossy compression techniques such as Vorbis and MP3. Compression ratios are similar to those for generic lossless data compression (around 50–60% of original size [5]), and substantially less than for lossy compression, which typically yield 5–20% of original size.[6]

The primary application areas of lossless encoding are:

Archives
For archival purposes it is generally desired to preserve the source material exactly (i.e., at 'best possible quality').
Editing
Audio engineers use lossless compression for audio editing to avoid digital generation loss.
High fidelity playback
Audiophiles prefer lossless compression formats to avoid compression artifacts.
Creating master copies for mass-produced audio
High quality losslessly compressed master copies of recordings are used to produce lossily compressed versions for digital audio players. As formats and encoders improve, updated lossily compressed files may be generated from the lossless master.
As file storage and communications bandwidth have become less expensive and more available, lossless audio compression has become more popular.[citation needed]
Formats

Shorten was an early lossless format; newer ones include Free Lossless Audio Codec (FLAC), Apple's Apple Lossless, MPEG-4 ALS, Windows Media Audio 9 Lossless (WMA Lossless), Monkey's Audio, and TTA. See list of lossless codecs for a complete list.

Some audio formats feature a combination of a lossy format and a lossless correction; this allows stripping the correction to easily obtain a lossy file. Such formats include MPEG-4 SLS (Scalable to Lossless), WavPack, and OptimFROG DualStream.

Some formats are associated with a technology, such as:

Difficulties in lossless compression of audio data

It is difficult to maintain all the data in an audio stream and achieve substantial compression. First, the vast majority of sound recordings are highly complex, recorded from the real world. As one of the key methods of compression is to find patterns and repetition, more chaotic data such as audio doesn't compress well. In a similar manner, photographs compress less efficiently with lossless methods than simpler computer-generated images do.[citation needed] But interestingly, even computer generated sounds can contain very complicated waveforms that present a challenge to many compression algorithms. This is due to the nature of audio waveforms, which are generally difficult to simplify without a (necessarily lossy) conversion to frequency information, as performed by the human ear.

The second reason is that values of audio samples change very quickly, so generic data compression algorithms don't work well for audio, and strings of consecutive bytes don't generally appear very often. However, convolution with the filter [-1 1] (that is, taking the first derivative) tends to slightly whiten (decorrelate, make flat) the spectrum, thereby allowing traditional lossless compression at the encoder to do its job; integration at the decoder restores the original signal. Codecs such as FLAC, Shorten and TTA use linear prediction to estimate the spectrum of the signal. At the encoder, the estimator's inverse is used to whiten the signal by removing spectral peaks while the estimator is used to reconstruct the original signal at the decoder.

Evaluation criteria

Lossless audio codecs have no quality issues, so the usability can be estimated by

  • Speed of compression and decompression
  • Degree of compression
  • Robustness and error correction
  • Product support

Lossy audio compression

Comparison of acoustic spectrograms of a song in an uncompressed format and various lossy formats. The fact that the lossy spectrograms are different from the uncompressed one indicates that they are in fact lossy, but nothing can be assumed about the effect of the changes on perceived quality.

Lossy audio compression is used in a wide range of applications. In addition to the direct applications (mp3 players or computers), digitally compressed audio streams are used in most video DVDs; digital television; streaming media on the internet; satellite and cable radio; and increasingly in terrestrial radio broadcasts. Lossy compression typically achieves far greater compression than lossless compression (data of 5 percent to 20 percent of the original stream, rather than 50 percent to 60 percent), by discarding less-critical data.

The innovation of lossy audio compression was to use psychoacoustics to recognize that not all data in an audio stream can be perceived by the human auditory system. Most lossy compression reduces perceptual redundancy by first identifying sounds which are considered perceptually irrelevant, that is, sounds that are very hard to hear. Typical examples include high frequencies, or sounds that occur at the same time as louder sounds. Those sounds are coded with decreased accuracy or not coded at all.

Due to the nature of lossy algorithms, audio quality suffers when a file is decompressed and recompressed (digital generation loss). This makes lossy compression unsuitable for storing the intermediate results in professional audio engineering applications, such as sound editing and multitrack recording. However, they are very popular with end users (particularly MP3), as a megabyte can store about a minute's worth of music at adequate quality.

Coding methods

In order to determine what information in an audio signal is perceptually irrelevant, most lossy compression algorithms use transforms such as the modified discrete cosine transform (MDCT) to convert time domain sampled waveforms into a transform domain. Once transformed, typically into the frequency domain, component frequencies can be allocated bits according to how audible they are. Audibility of spectral components is determined by first calculating a masking threshold, below which it is estimated that sounds will be beyond the limits of human perception.

The masking threshold is calculated using the absolute threshold of hearing and the principles of simultaneous masking—the phenomenon wherein a signal is masked by another signal separated by frequency, and, in some cases, temporal masking—where a signal is masked by another signal separated by time. Equal-loudness contours may also be used to weight the perceptual importance of different components. Models of the human ear-brain combination incorporating such effects are often called psychoacoustic models.

Other types of lossy compressors, such as the linear predictive coding (LPC) used with speech, are source-based coders. These coders use a model of the sound's generator (such as the human vocal tract with LPC) to whiten the audio signal (i.e., flatten its spectrum) prior to quantization. LPC may also be thought of as a basic perceptual coding technique; reconstruction of an audio signal using a linear predictor shapes the coder's quantization noise into the spectrum of the target signal, partially masking it.

Usability

Usability of lossy audio codecs is determined by:

  • Perceived audio quality
  • Compression factor
  • Speed of compression and decompression
  • Inherent latency of algorithm (critical for real-time streaming applications; see below)
  • Product support

Lossy formats are often used for the distribution of streaming audio, or interactive applications (such as the coding of speech for digital transmission in cell phone networks). In such applications, the data must be decompressed as the data flows, rather than after the entire data stream has been transmitted. Not all audio codecs can be used for streaming applications, and for such applications a codec designed to stream data effectively will usually be chosen.

Latency results from the methods used to encode and decode the data. Some codecs will analyze a longer segment of the data to optimize efficiency, and then code it in a manner that requires a larger segment of data at one time in order to decode. (Often codecs create segments called a "frame" to create discrete data segments for encoding and decoding.) The inherent latency of the coding algorithm can be critical; for example, when there is two-way transmission of data, such as with a telephone conversation, significant delays may seriously degrade the perceived quality.

In contrast to the speed of compression, which is proportional to the number of operations required by the algorithm, here latency refers to the number of samples which must be analysed before a block of audio is processed. In the minimum case, latency is 0 zero samples (e.g., if the coder/decoder simply reduces the number of bits used to quantize the signal). Time domain algorithms such as LPC also often have low latencies, hence their popularity in speech coding for telephony. In algorithms such as MP3, however, a large number of samples have to be analyzed in order to implement a psychoacoustic model in the frequency domain, and latency is on the order of 23 ms (46 ms for two-way communication).

Speech encoding

Speech encoding is an important category of audio data compression. The perceptual models used to estimate what a human ear can hear are generally somewhat different from those used for music. The range of frequencies needed to convey the sounds of a human voice are normally far narrower than that needed for music, and the sound is normally less complex. As a result, speech can be encoded at high quality using relatively low bit rates.

This is accomplished, in general, by some combination of two approaches:

  • Only encoding sounds that could be made by a single human voice.
  • Throwing away more of the data in the signal—keeping just enough to reconstruct an "intelligible" voice rather than the full frequency range of human hearing.

Perhaps the earliest algorithms used in speech encoding (and audio data compression in general) were the A-law algorithm and the µ-law algorithm.

History

Solidyne 922: The world's first commercial audio bit compression card for PC, 1990

A literature compendium for a large variety of audio coding systems was published in the IEEE Journal on Selected Areas in Communications (JSAC), February 1988. While there were some papers from before that time, this collection documented an entire variety of finished, working audio coders, nearly all of them using perceptual (i.e. masking) techniques and some kind of frequency analysis and back-end noiseless coding.[7] Several of these papers remarked on the difficulty of obtaining good, clean digital audio for research purposes. Most, if not all, of the authors in the JSAC edition were also active in the MPEG-1 Audio committee.

The world's first commercial broadcast automation audio compression system was developed by Oscar Bonello, an Engineering professor at the University of Buenos Aires.[8] In 1983, using the psychoacoustic principle of the masking of critical bands first published in 1967,[9] he started developing a practical application based on the recently developed IBM PC computer, and the broadcast automation system was launched in 1987 under the name Audicom. 20 years later, almost all the radio stations in the world were using similar technology, manufactured by a number of companies.

Video

Video compression refers to reducing the amount of data used to represent digital video images, and is a combination of spatial image compression and temporal motion compensation. Video compression is an example of the concept of source coding in Information theory. This article deals with its applications: compressed video can effectively reduce the bandwidth required to transmit video via terrestrial broadcast, via cable TV, or via satellite TV services.

Video quality

Most video compression is lossy: it operates on the premise that much of the data present before compression is not necessary for achieving good perceptual quality. For example, DVDs use a video coding standard called MPEG-2 that can compress video data by 15 to 30 times, while still producing a picture quality that is generally considered high-quality for standard-definition video. Video compression is a tradeoff between disk space, video quality, and the cost of hardware required to decompress the video in a reasonable time. However, if the video is overcompressed in a lossy manner, visible (and sometimes distracting) artifacts can appear.

Video compression typically operates on square-shaped groups of neighboring pixels, often called macroblocks. These pixel groups or blocks of pixels are compared from one frame to the next and the video compression codec (encode/decode scheme) sends only the differences within those blocks. This works extremely well if the video has no motion. A still frame of text, for example, can be repeated with very little transmitted data. In areas of video with more motion, more pixels change from one frame to the next. When more pixels change, the video compression scheme must send more data to keep up with the larger number of pixels that are changing. If the video content includes an explosion, flames, a flock of thousands of birds, or any other image with a great deal of high-frequency detail, the quality will decrease, or the variable bitrate must be increased to render this added information with the same level of detail.

The programming provider has control over the amount of video compression applied to their video programming before it is sent to their distribution system. DVDs, Blu-ray discs, and HD DVDs have video compression applied during their mastering process, though Blu-ray and HD DVD have enough disc capacity that most compression applied in these formats is light, when compared to such examples as most video streamed on the internet, or taken on a cellphone. Software used for storing video on hard drives or various optical disc formats will often have a lower image quality. High-bitrate video codecs with little or no compression exist for video post-production work, but create very large files and are thus almost never used for the distribution of finished videos. Once excessive lossy video compression compromises image quality, it is impossible to restore the image to its original quality.

Theory

Video is basically a three-dimensional array of color pixels. Two dimensions serve as spatial (horizontal and vertical) directions of the moving pictures, and one dimension represents the time domain. A data frame is a set of all pixels that correspond to a single time moment. Basically, a frame is the same as a still picture.

Video data contains spatial and temporal redundancy. Similarities can thus be encoded by merely registering differences within a frame (spatial), and/or between frames (temporal). Spatial encoding is performed by taking advantage of the fact that the human eye is unable to distinguish small differences in color as easily as it can perceive changes in brightness, so that very similar areas of color can be "averaged out" in a similar way to jpeg images.[10] With temporal compression only the changes from one frame to the next are encoded as often a large number of the pixels will be the same on a series of frames.

Lossless compression

Some forms of data compression are lossless. This means that when the data is decompressed, the result is a bit-for-bit perfect match with the original. While lossless compression of video is possible, it is rarely used, as lossy compression results in far higher compression ratios at an acceptable level of quality.

Intraframe versus interframe compression

One of the most powerful techniques for compressing video is interframe compression. Interframe compression uses one or more earlier or later frames in a sequence to compress the current frame, while intraframe compression uses only the current frame, which is effectively image compression.

The most commonly used method works by comparing each frame in the video with the previous one. If the frame contains areas where nothing has moved, the system simply issues a short command that copies that part of the previous frame, bit-for-bit, into the next one. If sections of the frame move in a simple manner, the compressor emits a (slightly longer) command that tells the decompresser to shift, rotate, lighten, or darken the copy: a longer command, but still much shorter than intraframe compression. Interframe compression works well for programs that will simply be played back by the viewer, but can cause problems if the video sequence needs to be edited.

Since interframe compression copies data from one frame to another, if the original frame is simply cut out (or lost in transmission), the following frames cannot be reconstructed properly. Some video formats, such as DV, compress each frame independently using intraframe compression. Making 'cuts' in intraframe-compressed video is almost as easy as editing uncompressed video: one finds the beginning and ending of each frame, and simply copies bit-for-bit each frame that one wants to keep, and discards the frames one doesn't want. Another difference between intraframe and interframe compression is that with intraframe systems, each frame uses a similar amount of data. In most interframe systems, certain frames (such as "I frames" in MPEG-2) aren't allowed to copy data from other frames, and so require much more data than other frames nearby.

It is possible to build a computer-based video editor that spots problems caused when I frames are edited out while other frames need them. This has allowed newer formats like HDV to be used for editing. However, this process demands a lot more computing power than editing intraframe compressed video with the same picture quality.

Current forms

Today, nearly all commonly used video compression methods (e.g., those in standards approved by the ITU-T or ISO) apply a discrete cosine transform (DCT) for spatial redundancy reduction. Other methods, such as fractal compression, matching pursuit and the use of a discrete wavelet transform (DWT) have been the subject of some research, but are typically not used in practical products (except for the use of wavelet coding as still-image coders without motion compensation). Interest in fractal compression seems to be waning, due to recent theoretical analysis showing a comparative lack of effectiveness of such methods.[citation needed]

Timeline

The following table is a partial history of international video compression standards.

History of Video Compression Standards
Year Standard Publisher Popular Implementations
1984 H.120 ITU-T
1990 H.261 ITU-T Videoconferencing, Videotelephony
1993 MPEG-1 Part 2 ISO, IEC Video-CD
1995 H.262/MPEG-2 Part 2 ISO, IEC, ITU-T DVD Video, Blu-ray, Digital Video Broadcasting, SVCD
1996 H.263 ITU-T Videoconferencing, Videotelephony, Video on Mobile Phones (3GP)
1999 MPEG-4 Part 2 ISO, IEC Video on Internet (DivX, Xvid ...)
2003 H.264/MPEG-4 AVC ISO, IEC, ITU-T Blu-ray, Digital Video Broadcasting, iPod Video, HD DVD
2008 VC-2 (Dirac) ISO, BBC Video on Internet, HDTV broadcast, UHDTV

See also

References

  1. ^ a b "The World’s Technological Capacity to Store, Communicate, and Compute Information", especially Supporting online material, Martin Hilbert and Priscila López (2011), Science (journal), 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.html
  2. ^ Rationale for a Large Text Compression Benchmark
  3. ^ RFC 3284
  4. ^ Korn, D.G.; Vo, K.P. (1995), B. Krishnamurthy, ed., Vdelta: Differencing and Compression, Practical Reusable Unix Software, John Wiley & Sons 
  5. ^ Comparison of lossless codecs on the FLAC's website
  6. ^ Comparison of lossy codecs
  7. ^ Journal on Selected Areas in Communications, February 1988
  8. ^ Solidyne... 40 years of innovation
  9. ^ The Ear as a Communication Receiver. English translation of Das Ohr als Nachrichtenempfänger by Eberhard Zwicker and Richard Feldtkeller. Translated from German by Hannes Müsch, Søren Buus, and Mary Florentine. Originally published in 1967; Translation published in 1999
  10. ^ http://www.faqs.org/faqs/jpeg-faq/part1/

External links


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