  Inversions of rotational splittings have shown that the surface layers and
the so-called solar tachocline at the base of the convection zone are regions
in which high radial gradients of the rotation rate occur. The usual
regularization methods tend to smooth out every high gradients in the solution
and may not be appropriate for the study of a zone like the tachocline. In this
paper we use nonlinear regularization methods that are developed for
edge-preserving regularization in computed imaging (e.g. Blanc-F\'eraud et al.
1995) and we apply them in the helioseismic context of rotational inversions.
