Haar wavelet basis

1. What is Haar basis?
2. What is a wavelet basis?
3. What is Haar wavelet transform?
4. What is Haar wavelet used for?

What is Haar basis?

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 a wavelet basis?

A wavelet is a waveform of effectively limited duration that has an average value of zero and nonzero norm. Many signals and images of interest exhibit piecewise smooth behavior punctuated by transients.

What is Haar wavelet transform?

The Haar transform is one of the earliest examples of what is known now as a compact, dyadic, orthonormal wavelet transform [7,33]. The Haar function, being an odd rectangular pulse pair, is the simplest and oldest orthonormal wavelet with compact support.

What is Haar wavelet used for?

Haar wavelet compression is an efficient way to perform both lossless and lossy image compression. It relies on averaging and differencing values in an image matrix to produce a matrix which is sparse or nearly sparse.