Haar transform definition

The Haar transform is the simplest of the wavelet transforms. This transform cross-multiplies a function against the Haar wavelet with various shifts and stretches, like the Fourier transform cross-multiplies a function against a sine wave with two phases and many stretches.

1. What is Haar wavelet used for?
2. How feature is generated using Haar transform?
3. What is meant by wavelet transform?
4. What is a Haar matrix?

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.

How feature is generated using Haar transform?

The first basis function creates a running sum of the input data, the second creates a difference between the first two and the second two data samples, the third creates a difference between the first two data points, and similarly the basis function in the bottom row does the same for the last two data points.

What is meant by wavelet transform?

Wavelet transforms are mathematical tools for analyzing data where features vary over different scales. For signals, features can be frequencies varying over time, transients, or slowly varying trends. For images, features include edges and textures.

What is a Haar matrix?

The Haar matrix is the 2x2 DCT matrix, so inversly, you can treat the NxN DCT(II) matrix as the Haar matrix for that block size. Or if the N is dyadic, N=2^n, then you might be asking for the transform matrix for n stages of the Haar transform.