  In this paper, a restricted transverse ray transform acting on vector and
symmetric $m$-tensor fields is studied. We developed inversion algorithms using
restricted transverse ray transform data to recover symmetric $m$-tensor fields
in $\mathbb{R}^3$ and vector fields in $\mathbb{R}^n$. We restrict the
transverse ray transform to all lines going through a fixed curve $\gamma$ that
satisfies the Kirillov-Tuy condition. We show that the known restricted data
can be used to reconstruct a specific weighted Radon transform of the unknown
vector/tensor field's components, which we then use to explicitly recover the
unknown field.
