  Consider a compact Riemannian manifold in dimension $n$ with strictly convex
boundary. We show the local invertibility near a boundary point of the
transverse ray transform of $2$ tensors for $n\geq 3$ and the mixed ray
transform of $2+2$ tensors for $n=3$. When the manifold admits a strictly
convex function, this local invertibility result leads to global invertibility.
