Image Compression using the Wavelet Decomposition
After downloading compress.jar, please execute it by double-clicking, or typing "java -jar compress.jar".
If the above application does not start, please install Java from www.java.com.
This applet demonstrates the image compression with the wavelet decomposition.
The so-called JPEG2000 is based on this method.
As shown in the page of "edge detection with the wavelet decomposition", the original image is reconstructed from the low-freq. and high-freq. components with the inverse wavelet transformation.
Typically, the high-freq components (or, wavelet coefficients) distribute
around 0 according to the bell-shaped distribution like Gaussian.
Lets denote the standard deviation of the distribution as σ.
By discarding small wavelet coefficients,
the amount of the data can be reduced.
The lower-left image shows points
whose wavelet coefficients are larger than σ.
By reconstructing the image with only large wavelet coefficients,
the compressed image is obtained.
When the high-level wavelet decomposition is applied,
the quality of the compressed image is low because the data are too much reduced.
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