I read following paper : [2019, Emilie Chouzenoux, A Proximal Interior Point Algorithm with Applications to Image Processing].
The problem is constructed as Proximal interior point method, and solved by the proposed PIPA algorithm. In the objective function, as a regularization, they used Wavelet decomposition operator.
But in the paper, they said : " we selected an orthogonal Daubechies 4 wavelet decomposition performed over 2 resolution levels", and they used the detail coefficients of level 2 as above picture.
I can get detail coefficients over several levels. But in this case we should used matrix "W" to get it, and this is strange for me.
Can you explain how to make such matrix? Thank you!
Best Answer
Although you can construct the matrix for the wavelet transform, I'd say it's inadviseable. Most software packages have implementations of the discrete wavelet transform (and the inverse wavelet transform) implemented. These will be far more numerically stable (and probably faster than constructing the matrix itself), not to mention you will save CPU memory as well.
As my numerical analysis professor would always say "Don't reinvent the wheel. use the tools that were built for the job!"