  We study the problem of inverting a restricted transverse ray transform to
recover a symmetric $m$-tensor field in $\mathbb{R}^3$ using microlocal
analysis techniques. More precisely, we prove that a symmetric $m$-tensor field
can be recovered up to a known singular term and a smoothing term if its
transverse ray transform is known along all lines intersecting a fixed smooth
curve satisfying the Kirillov-Tuy condition.
