Hi all,
I'm looking to do denoising on a set of non-natural images; these
images come from experiments in visual research. As it turns out, to
find out the truly important components in the image, the correct
statistical procedure is to hard threshold the image according to a
lower and upper bound (a z-value). However, in luminance (pixel)
space, that's a pretty poor way of denoising. Hence I've looked at
wavelet methods, applying instead the threshold on the wavelet
coefficients. However I have quite a few restraints here. First, the
artifacts of taking out most coefficients should be well behaved,
predictable, easily identifiable. This immediately rules out Haar,
Daubechies, and such wavelets.
Basically I need the wavelets to be highly continuous, symmetric,
translation-invariant (no aliasing) and have good reconstruction
properties. Of course I'm well aware that that's simply impossible
with orthonormal wavelets, which is why I've looked at overcomplete
wavelet sets. Biorthogonal wavelets have given poor results. Laplacian
pyramid and Simoncelli's steered pyramid, however, have worked pretty
well so far. For the stats procedure to work well, it needs two
things: 1) the representation shouldn't be _too_ overcomplete, as the
threshold goes up exponentially with number of dimensions and 2) the
representation should be as sparse as possible. If this weren't tied
to a statistical test, I could use better methods of denoising than a
hard threshold; but I'm afraid that's simply not possible in this
case.
So, apart from Laplacian and steerable pyramids, do any of you guys
know any overcomplete wavelet or wavelet-like representations that
have the properties I'm looking for? Thanks,
Patrick
