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Wavelet compression is a form of data compression well suited for image compression (sometimes also video compression and audio compression). The goal is to store image data in as little space as possible in a file. A certain loss of quality is accepted (lossy compression). In computer science, data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than a more obvious representation would use, through use of specific encoding schemes. ...
Image compression is the application of data compression on digital images. ...
Video compression deals with the compression of digital video data. ...
Audio compression can mean two things: Audio data compression _ in which the amount of data in a recorded waveform is reduced for transmission. ...
A file in a computer system is a stream (sequence) of bits stored as a single unit, typically in a file system on disk or magnetic tape. ...
A lossy data compression method is one where compressing a file and then decompressing it retrieves a file that may well be different to the original, but is close enough to be useful in some way. ...
Using a wavelet transform, the wavelet compression methods are better at representing transients, such as percussion sounds in audio, or high-frequency components in two-dimensional images, for example an image of stars on a night sky. This means that the transient elements of a data signal can be represented by a smaller amount of information than would be the case if some other transform, such as the more widespread discrete cosine transform, had been used. The wavelet transform is a transformation to basis functions that are localized in scale and in time as well (where the Fourier transform is only localized in frequency, never giving any information about where in space or time the frequency happens). ...
Transient means passing with time. ...
The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. ...
Wavelet compression is not good for all kinds of data: transient signal characteristics mean good wavelet compression - smooth, periodic signals are better compressed by other methods.
Method
First a wavelet transform is applied. This produces as many coefficients as there are pixels in the image (i.e.: there is no compression yet since it is only a transform). These coefficients can then be compressed more easily because the information is statistically concentrated in just a few coefficients. This principle is called transform coding. After that, the coefficients are quantized and the quantized values are entropy encoded and/or run length encoded. The wavelet transform is a transformation to basis functions that are localized in scale and in time as well (where the Fourier transform is only localized in frequency, never giving any information about where in space or time the frequency happens). ...
In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ...
A pixel (pix, 1932 abbreviation of pictures, coined by Variety headline writers + element) is one of the many tiny dots that make up the representation of a picture in a computers memory. ...
In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ...
Transform coding is a type of data compression for natural data like audio signals or photographic images. ...
In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ...
Quantization of x using Q(x) = floor(Lx)/L. In digital signal processing, quantization is the process of approximating a continuous signal by a set of discrete symbols or integer values; that is, converting an analog signal to a digital one via analog-to-digital conversion. ...
An entropy encoding is a coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols. ...
Run-length encoding (RLE) is a very simple form of data compression in which runs of data (that is, sequences in which the same data value occurs in many consecutive data elements) are stored as a single data value and count, rather than as the original run. ...
Examples for wavelet compression:
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