Wavelet Transform energy preservation

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Brian 2014-11-21

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https://ww2.mathworks.cn/matlabcentral/answers/163766-wavelet-transform-energy-preservation

评论： Brian 2014-11-25

Some brief understanding of this topic is required as I describe my problem. In Wavelet image compression, one has two main components: an image and a Wavelet matrix. An important property of wavelets is that its inverse is also its transpose. Here are the matrices we're using * I=('kochflake.png'); * T1 is a 256x256 matrix whose inverse is its transpose * W=T1*double(I)*transpose(T1); When we compute W, we are not supposed to lose or gain energy. Here is our problem. Images are often of type uint8, and when computing many (large) numbers, the computer asks that the data be converted to double. I have tested these two different types and found that they have different energies.

*energy is defined as the sum of the squared elements of a matrix.

For image compression, this understanding is key in reducing data space required by the computer. So we come down to two unique problems:

#1 Which sumsqr algorithm is the correct one? uint8 method or double? #2 Why, when we run the program, do we get different energies for I and W?