Wavelet compression
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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).
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.
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. Some projects (such as Ogg Vorbis) aim at combining discrete cosine transform with a wavelet transform to produce a hybrid compression method that would be good at representing a mix of smooth signals and transients - as exhibited by most popular music, for example.
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.
Examples for wavelet compression: