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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. |