Lossless data compression wavelet

Discrete wavelet transform has been successfully applied for the compression of electrocardiograph (ECG) signals In this work, the high correlation between the corresponding wavelet coefficients of signals of successive cardiac cycles is utilized employing linear prediction.
Wavelet compression is not effective for all kinds of data.

Wavelet compression can be either lossless or lossy. Using a wavelet transform, the wavelet compression methods are adequate for representing transients, such as:

1. percussion sounds in audio
2. high-frequency components in two-dimensional images
3. for example an image of stars on a night sky

Notable implementations are JPEG 2000, DjVu and ECW for still images, JPEG XS, CineForm, and the BBC's Dirac.
The goal is to store image data in as little space as possible in a file.
Wavelet compression can be either lossless or lossy.

Embedded Zerotrees of Wavelet transforms ( EZW) is a lossy image compression algorithm.
At low bit rates, i.e. high compression ratios, most of the coefficients produced by a subband transform (such as:

1. the wavelet transform ) will be zero
2. very close to zero

‘Lossless’ data compression is a technique that reduces the size of files without affecting the image quality

There is a limit, however, to the amount of size reduction that can be achieved with lossless techniques, and thus ‘lossy’ compression is more common

In this chapter we discuss the role of wavelets as applied to lossy compression

It is evolving into an important technology for image manipulation

Another type of lossy compression goes under the label “denoising

In order to process an image, symmetric biorthogonal wavelets are used

These have two father and two mother wavelets, and are required in order tocompress a matrix of data

The Daubechies wavelet family is the mostwidely used wavelet for image compression, with six coefficients andbiorthogonality