OK... this has all been very good inputs. I've read through most of the posts about MLT and MMT and think I'm beginning to understand.
Both start w/ a wavelets decomposition of the image, using some basis / family of wavelets (I don't know enough about the various bases to understand the relative merits of them)... and it probably doesn't matter at this level what the choices are... they just work... which aint bad...
This produces an image of wavelets coefficients, which indicate how much of any given wavelet contributes to the image at and around that pixel. The coefficients can be positive or negative and probably nicely distribute around zero... but maybe there's a bias in one direction or the other based on image properties...??
ASSUMPTION: legitimate structure in the image is represented in the transform coefficients by larger absolute magnitudes... if this isn't correct, then my brain is in trouble... can someone confirm??
So in either method (MLT or MMT), the coefficients that are below the threshold value (which is given in MAD units, which is good), are replaced by calculated values, (I assume the calcuation only uses 'neighboring' coefficients that are above the MAD threshold value) then this is where the two methods diverge...
MLT seems to use a convolution around that 'bad' coefficient location (pixel) in the image, so uses some convolution kernel calculated over the local area... convolutions can seem to be complex, formaly being an integration over the function and the kernel, but they are linear so that conv(A + B) = conv(A) + conv(B) or conv(c * A) = c*conv(A) ... now I didn't know this, but these linear denoising or structure enhancements allow the Gibb's phenomenon so may be subject to significant ringing artifacts... hmmm... we learn something new every day...
MMT seems then to use a morphological median around that 'bad' coeffient location... this is a non-linear function... so 'not' subject to the Gibb's phenomenon... hmmm... no ringing !?? ... now I don't know if ANY AND ALL non-linear transforms (median is only the one used in MMT) cannot cause ringing, but that's a more mathematical discussion.... interesting but probably not useful in the present discussion
Can anyone on the PI team weigh in on what the neighborhood is over which the convolution and median are calculated in MLT and MMT respecively? Also, what kernel is used in MLT (I assume if I know the size for MMT then it's almost certainly a circular structuring element in the morphological operator)...
OK... so to be honest... I'd be willing to bet my descriptions above are closer to the true algorithms than my previous understandings, but I'm sure I'm wrong at some level(s)... If anyone wants to further edgumacate me on this that'd be great. I'm one of those folks who is EXTREMELY forgetteful, so it takes me a LONG time to learn w/o some understanding of what I'm working with... but if I understand the concepts underlying anything, that stuff stays with me forever and I can use those to figure out how to work things...
OK... then... what's the current understanding of the proper roles of the two tools? I kinda thought MLT was preferred for noise reduction and I've even been using it to enhance structures... but maybe that's not right... maybe I / we should migrate to MMT for these purposes !! What about other uses like breaking an image into ones containing only certain structure ranges ?
Thanx everybody for weighing in on this and helping me understand. Now for the fun stuff... I'm gonna take my latest image and test the two tools and see if the results conform with my new concepts and understandings !!
CYa
Jim