Application of Haar Wavelets on Medical Images

2. Principle Of Haar Wavelets

In 1909, ALFRED HAAR was created a special function called « Haar wavelets » (Figure 1) (Myung-Sin Song, 1991, Ronald A. DeVore & all, 1992, Kamrul Hasan Talukder & all, 2007). This type of waveletallows a decomposition of data. Specifically, in image processing, it is used for compressing.

Figure 1.

Haar wavelet

Consider the image M to be compressed. For a compression level h, Haar wavelets divide the compressed imageM_h-1 at the level h-1 into four blocks (Figure 2): The left upper block representing the compressed image M_h and the other containing the details ((horizontal DH_h, vertical DV_h and diagonal DD_h).

Figure 2.

Compressing using Haar wavelets

Obtaining the compressed image at level h is based on the compressed image at level h-1.

The compressed image is computedas follows:

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  : Compressed image for a level h

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  :Haar wavelets coefficients for a level h

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  : Transposed of