  We study an inverse problem involving the unique recovery of several lower
order anisotropic tensor perturbations of a polyharmonic operator in a bounded
domain from the knowledge of the Dirichlet to Neumann map on a part of
boundary. The uniqueness proof relies on the inversion of generalized momentum
ray transforms (MRT) for symmetric tensor fields, which we introduce for the
first time to study Calder\'on-type inverse problems. We construct suitable
complex geometric optics (CGO) solutions for the polyharmonic operators that
reduces the inverse problem to uniqueness results for a generalized MRT. The
uniqueness result and the inversion formula we prove for generalized MRT could
be of independent interest and we expect it to be applicable to other inverse
problems for higher order operators involving tensor perturbations.
