Haar wavelet transform

1. What is Haar wavelet transform?
2. What is Haar wavelet used for?
3. What is a wavelet transform in image processing?
4. What is a Haar matrix?

What is Haar wavelet transform?

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.

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.

What is a wavelet transform in image processing?

Wavelets based transform are mathematical tools which are used to extract information from images [12]. A significant benefit it has over Fourier transforms is temporal resolution which signifies that it can captures both frequency and location information of the images [13].

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.