Discrete Haar wavelet transform, fast and efficient method?

1. What is Haar wavelet method?
2. What is fast wavelet transform in image processing?
3. How Haar transform is related to wavelet transform?
4. What is discrete wavelet transform used for?

What is Haar wavelet method?

In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis.

What is fast wavelet transform in image processing?

The fast wavelet transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or wavelets.

How Haar transform is related to wavelet transform?

A Haar wavelet is the simplest type of wavelet. In discrete form, Haar wavelets are related to a mathematical operation called the Haar transform. The Haar transform serves as a prototype for all other wavelet transforms.

What is discrete wavelet transform used for?

The discrete wavelet transform has a huge number of applications in science, engineering, mathematics and computer science. Most notably, it is used for signal coding, to represent a discrete signal in a more redundant form, often as a preconditioning for data compression.