  The continuous wavelet transform has become a widely used tool in applied
science during the last decade. In this article we discuss some generalizations
coming from actions of closed subgroups of $\mathrm{GL}(n,\mathbb{R})$ acting
on $\mathbb{R}^n$. In particular, we propose a way to invert the wavelet
transform in the case where the stabilizer of a generic point in $\mathbb{R}^n$
is not compact, but a symmetric subgroup, a case that has not previously been
discussed in the literature.
