Juan - can you comment on the applicability of MMT and MLT for sharpening and where the older MMT is preferred over MLT for this purpose?
As Jim says, both are viable tools. However, there some important differences and facts that should always be taken into account:
- MMT is a ringing-free transformation. See
this tutorial. This property makes it particularly suitable for local contrast enhancement (aka sharpening). MLT, as any linear transform, suffers from ringing, although our deringing algorithms alleviate this problem.
- The counterpart to ringing is small artifacts that can be generated by MMT around image structures that are very different morphologically from the structuring elements used to apply median filters. With our implementation, however, this is usually a marginal problem, and even more marginal with astronomical images, where sharp linear edges and angles are rare. The key word here is
careful application.
- MMT works very well to sharpen small-scale structures. However, it does not work to enhance structures at medium and large scales, where it can generate large (and often not obvious) artifacts.
- The linear transforms implemented in MLT, including the Starlet (aka
á trous wavelet) and multiscale linear transforms, have the important advantage that they are isotropic, that is, they modify the image exactly the same way in all directions. This is not true for MMT, although our implementation is reasonably close to isotropic. Isotropy is a very important property to process astronomical images.
- MLT works very well at medium and large scales. It does not work so well at small scales, mainly as a result of its poor efficiency to isolate structures, compared to MMT.
- The Wavelet-median transform, which I implemented in MMT a few years ago, attempts to provide the best of both linear and nonlinear worlds: MMT for small high-contrast structures, and MLT for large-scale, low-contrast structures (such as the background).
Experimentation is always necessary, as well as knowing that each image poses different problems requiring different solutions. I hope this helps.