Discrete cosine transform in the context of Data compression

JPEG (/ˈdʒeɪpɛɡ/ JAY-peg, 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 image file formats. JPEG/Exif is the most common image format used by digital cameras and other photographic image capture devices; along with JPEG/JFIF, it is the most common format for storing and transmitting photographic images on the World Wide Web. These format variations are often not distinguished and are simply called JPEG.

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 Nasir Ahmed, T. Natarajan and K. R. Rao in 1974.

A video coding format (or sometimes video compression format) is an encoded format of digital video content, such as in a data file or bitstream. It typically uses a standardized video compression algorithm, most commonly based on discrete cosine transform (DCT) coding and motion compensation. A computer software or hardware component that compresses or decompresses a specific video coding format is a video codec.

Some video coding formats are documented by a detailed technical specification document known as a video coding specification. Some such specifications are written and approved by standardization organizations as technical standards, and are thus known as a video coding standard. There are de facto standards and formal standards.

Nasir Ahmed (born 1940) is an American electrical engineer and computer scientist. He is Professor Emeritus of Electrical and Computer Engineering at University of New Mexico (UNM). He is best known for inventing the discrete cosine transform (DCT) in the early 1970s. The DCT is the most widely used data compression transformation, the basis for most digital media standards (image, video and audio) and commonly used in digital signal processing. He also described the discrete sine transform (DST), which is related to the DCT.

Kamisetty Ramamohan Rao (1931 – 2021) was an Indian-American electrical engineer. He was a professor of Electrical Engineering at the University of Texas at Arlington (UT Arlington). Academically known as K. R. Rao, he is credited with the co-invention of discrete cosine transform (DCT), along with Nasir Ahmed and T. Natarajan due to their landmark publication, Discrete Cosine Transform.

Dolby Digital, originally synonymous with Dolby AC-3 (see below), is the name for a family of audio compression technologies developed by Dolby Laboratories. Called Dolby Stereo Digital until 1995, it uses lossy compression (except for Dolby TrueHD). The first use of Dolby Digital was to provide digital sound in cinemas from 35 mm film prints. It has since also been used for TV broadcast, radio broadcast via satellite, digital video streaming, DVDs, Blu-ray discs and game consoles.

Dolby AC-3 was the original version of the Dolby Digital codec. The basis of the Dolby AC-3 multi-channel audio coding standard is the modified discrete cosine transform (MDCT), a lossy audio compression algorithm. It is a modification of the discrete cosine transform (DCT) algorithm, which was proposed by Nasir Ahmed in 1972 for image compression. The DCT was adapted into the MDCT by J.P. Princen, A.W. Johnson and Alan B. Bradley at the University of Surrey in 1987.

Advanced Video Coding (AVC), also referred to as H.264 or MPEG-4 Part 10, is a video compression standard based on block-oriented, motion-compensated coding. It is by far the most commonly used format for the recording, compression, and distribution of video content, used by 79% of video industry developers as of December 2024. It supports a maximum resolution of 8K UHD.

The intent of the H.264/AVC project was to create a standard capable of providing good video quality at substantially lower bit rates than previous standards (i.e., half or less the bit rate of MPEG-2, H.263, or MPEG-4 Part 2), without increasing the complexity of design so much that it would be impractical or excessively expensive to implement. This was achieved with features such as a reduced-complexity integer discrete cosine transform (integer DCT), variable block-size segmentation, and multi-picture inter-picture prediction. An additional goal was to provide enough flexibility to allow the standard to be applied to a wide variety of applications on a wide variety of networks and systems, including low and high bit rates, low and high resolution video, broadcast, DVD storage, RTP/IP packet networks, and ITU-T multimedia telephony systems. The H.264 standard can be viewed as a "family of standards" composed of a number of different profiles, although its "High profile" is by far the most commonly used format. A specific decoder decodes at least one, but not necessarily all profiles. The standard describes the format of the encoded data and how the data is decoded, but it does not specify algorithms for encoding—that is left open as a matter for encoder designers to select for themselves, and a wide variety of encoding schemes have been developed. H.264 is typically used for lossy compression, although it is also possible to create truly lossless-coded regions within lossy-coded pictures or to support rare use cases for which the entire encoding is lossless.

A compression artifact (or artefact) is a noticeable distortion of media (including images, audio, and video) caused by the application of lossy compression. Lossy data compression involves discarding some of the media's data so that it becomes small enough to be stored within the desired disk space or transmitted (streamed) within the available bandwidth (known as the data rate or bit rate). If the compressor cannot store enough data in the compressed version, the result is a loss of quality, or introduction of artifacts. The compression algorithm may not be intelligent enough to discriminate between distortions of little subjective importance and those objectionable to the user.

The most common digital compression artifacts are DCT blocks, caused by the discrete cosine transform (DCT) compression algorithm used in many digital media standards, such as JPEG, MP3, and MPEG video file formats. These compression artifacts appear when heavy compression is applied, and occur often in common digital media, such as DVDs, common computer file formats such as JPEG, MP3 and MPEG files, and some alternatives to the compact disc, such as Sony's MiniDisc format. Uncompressed media (such as on Laserdiscs, Audio CDs, and WAV files) or losslessly compressed media (such as FLAC or PNG) do not suffer from compression artifacts.

Motion compensation in computing is an algorithmic technique used to predict a frame in a video given the previous and/or future frames by accounting for motion of the camera and/or objects in the video. It is employed in the encoding of video data for video compression, for example in the generation of MPEG-2 files. Motion compensation describes a picture in terms of the transformation of a reference picture to the current picture. The reference picture may be previous in time or even from the future. When images can be accurately synthesized from previously transmitted/stored images, the compression efficiency can be improved.

Motion compensation is one of the two key video compression techniques used in video coding standards, along with the discrete cosine transform (DCT). Most video coding standards, such as the H.26x and MPEG formats, typically use motion-compensated DCT hybrid coding, known as block motion compensation (BMC) or motion-compensated DCT (MC DCT).

High Efficiency Video Coding (HEVC), also known as H.265 and MPEG-H Part 2, is a proprietary video compression standard designed as part of the MPEG-H project as a successor to the widely used Advanced Video Coding (AVC, H.264, or MPEG-4 Part 10). The standard was published in 2013. In comparison to AVC, HEVC offers from 25% to 50% better data compression at the same level of video quality, or substantially improved video quality at the same bit rate. It supports resolutions up to 8192×4320, including 8K UHD, and unlike the primarily eight-bit AVC, HEVC's higher-fidelity Main 10 profile has been incorporated into nearly all supporting hardware. The High Efficiency Image Format (HEIF) is a container format whose default codec is HEVC.

While AVC uses the integer discrete cosine transform (DCT) with 4×4 and 8×8 block sizes, HEVC uses both integer DCT and discrete sine transform (DST) with varied block sizes between 4×4 and 32×32.

The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where subsequent blocks are overlapped so that the last half of one block coincides with the first half of the next block. This overlapping, in addition to the energy-compaction qualities of the DCT, makes the MDCT especially attractive for signal compression applications, since it helps to avoid artifacts stemming from the block boundaries. As a result of these advantages, the MDCT is the most widely used lossy compression technique in audio data compression. It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), High-Definition Coding (HDC), LDAC, Dolby AC-4, and MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.

The discrete cosine transform (DCT) was first proposed by Nasir Ahmed in 1972, and demonstrated by Ahmed with T. Natarajan and K. R. Rao in 1974. The MDCT was later proposed by John P. Princen, A.W. Johnson and Alan B. Bradley at the University of Surrey in 1987, following earlier work by Princen and Bradley (1986) to develop the MDCT's underlying principle of time-domain aliasing cancellation (TDAC), described below. (There also exists an analogous transform, the MDST, based on the discrete sine transform, as well as other, rarely used, forms of the MDCT based on different types of DCT or DCT/DST combinations.)

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 ISO/IEC 15444-1 conforming files and .jpx or .jpf for the extended part-2 specifications, published as ISO/IEC 15444-2. The 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's submission in 1995 of the CREW (Compression with Reversible Embedded Wavelets) algorithm to the standardization effort of JPEG LS. Ultimately the LOCO-I algorithm was selected as the basis for JPEG LS, but many of the features of CREW ended up in the JPEG 2000 standard.

In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample.

The DST is related to the discrete cosine transform (DCT), which is equivalent to a DFT of real and even functions. See the DCT article for a general discussion of how the boundary conditions relate the various DCT and DST types. Generally, the DST is derived from the DCT by replacing the Neumann condition at x=0 with a Dirichlet condition. Both the DCT and the DST were described by Nasir Ahmed, T. Natarajan, and K.R. Rao in 1974. The type-I DST (DST-I) was later described by Anil K. Jain in 1976, and the type-II DST (DST-II) was then described by H.B. Kekra and J.K. Solanka in 1978.