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# wavelet compression

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wavelet compression is a form of data compression well suited for image compression

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### wavelet compression

1. 1. Submitted by K.Priyadarsini II M.SC(CS& IT) N.Pandimeena II M.SC(CS& IT) V.Sarmila II M.SC(CS& IT) Nadar saraswathi college of arts and science, Theni.
2. 2. wavelet compression  Wavelet compression is a form of data compression well suited for image compression (sometimes also video compression and audio compression).  Notable implementations are JPEG2000 , Divu and ECW for still images, Cine Form, and the BBC's Dirac.  The goal is to store image data in as little space as possible in a file.  Wavelet compression can be either lossless or lossy.  Using a wavelet transform, the wavelet compression methods are adequate for representing transients.  such as percussion sounds in audio, or high-frequency components in two-dimensional images, for example an image of stars on a night sky.
3. 3. Method  First a wavelet transform is applied.  This produces as many coefficients as there are pixels in the image (i.e., there is no compression yet since it is only a transform).  These coefficients can then be compressed more easily because the information is statistically concentrated in just a few coefficients.  This principle is called transform coding.  After that, the coefficients are quantized and the quantized values are entropy encoded and/or run length encoded.
4. 4. The Idea  The idea is to start first with a gray scale image, and do like you would proceed for a PNG image compressor: pick your buffer and group the pixels in tiles of 2x2.  Now, if you only store the average color of the four pixels of each tile you are already compressing by 1:4. Good. Of course the image resolution has decreased.  Let's fix it by storing the real value of the 4 pixels in a compact manner.  Because these pixels are physically near to each other, we can pretty safely assume their colors will be similar to that average color that we already encoded.  So, instead of storing these pixels as full gray scale values, let's store only the amount by which they are different to the average color
5. 5. The Details  Well, not quite. Wavelets are a complex signal processing tool, and what we are doing here is nothing but scratching the very surface of the thing.  In fact, what we are doing is to use one of the many possible Wavelets basis, the Haar wavelet to be more precise.  But we are not going into filter-banks and dsp stuff here - instead we just will see how I implemented this simple multilevel color encoding technique and how I had my image compressed into my demo.
6. 6. Color Images  So far we have compressed gray scale images only.  For color images we are gonna use a very standard method that makes storing color very unexpensive, almost for free.  The naive approach of decomposing the rgb images in three independent gray scale images is a very bad idea, you should NEVER do that. Instead we are going to use the popular luma/chroma decomposition, as JPG does.