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Maximum Entropy Method – 2 – Wavelets

Written By: Jean-Paul Cipria - Juin• 03•16

Wavelets is a compression transform for signals. Then do wavelets perform the maximum absolute compression ?

Wavelet : Haar-2 - Diagonal

Wavelet : Haar-2 – Diagonal

Wavelets Signals

First we read a simple image with vertical and horizontal and diagonal lines to see how HAAR decomposition transformation held the picture. DWT is a MATLAB wavelet transformation function. Therefore IDWT is the inverse transformation.

Images sizes

The input image is 20 kO size in jpg format. JPG is already compressed. Then when we transforms the input image with HAAR transformation then the result is 11 kO size. HAAR transformation is able to gain a factor 2 compression compared to JPG picture.

Conclusion

The input image contains redondant informations. We must then eliminate this by a space transformation like HAAR or DB wavelet. But what is the Entropy then ? What actions we had to do to know how much informations need to be compressed or how much informations is redondant ?

Scaling function phi

Wavelet - Daubechies Scaling Function Phi

Wavelet – Daubechies Scaling Function Phi

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© Jean-Paul Cipria
Senior Engineer-Physicist
03/06/2016

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