I need to use wavelet based method to remove Gaussian white noise on
an image. I have some confusion and would like to ask you:
1. What wavelet basis I should choose for decomposing the image? I
intend to use Haar , DB2, db3, db4 to test the SNR to see what is the
best. However I am considering for Gaussian Noise, if there are some
best wavelet bases for this task, if their properties (i.e support,
vanishing moments and symmetriness) affect anything on the quality of
the filter ( specifically the SNR).
2. I heard about the so called " best wavelet basis" which we choose
from a wavelet tree which can be the best to approximate the signal.
There are some algorithm to search for it. I am wondering if I need to
use that "best wavelet basis" for my Gaussian Noise filter based
wavelet method. What criteria I should choose to search for that best
3. How deep should I decompose the image, specifically do I need to
decompose it until the maximum of the possible scale j (Log2 N, I
4. Is soft thresholding is always better than hard thresholding?
Thank you very much.