Shapelet failures
For galaxies with steep cores and moderate to large ellipiticties the shapelet decompositions (right, nmax=20) fails to reproduce the shape well. Prominent artifacts are the rings you can see on the right image. Also the core regions is too extended and has too shallow a profile.
In a weak-lensing analysis, we often don't know if a galaxy has a steep or a shallow radial profile, so we cannot exclude such galaxies. It becomes therefore relevant how much their shear/ellipticity estimates are off.
For the plot to the right we simulated galaxies with different radial profiles (described by the Sérsic profile index ns) and different ellipticities ε. We than looked at difference between the shear estimate and the true shear. It is evident that shapelets become increasingly insensitive to shear when the Sérsic index rises. The galaxy at the top of this page has and ns≈ 4.