  In this paper we study elimination of imaginaries in some classes of pure
ordered abelian groups. For the class of ordered abelian groups with bounded
regular rank (equivalently with finite spines) we obtain weak elimination of
imaginaries once we add sorts for the quotient groups $\Gamma/ \Delta$ for each
definable convex subgroup $\Delta$, and sorts for the quotient groups $\Gamma/
\Delta+ l\Gamma$ where $\Delta$ is a definable convex subgroup and $l \in
\mathbb{N}_{\geq 2}$. We refer to these sorts as the \emph{quotient sorts}. For
the dp-minimal case we obtain a complete elimination of imaginaries, if we also
add constants to distinguish the elements of the finite groups $\Gamma/\ell
\Gamma$ for each $ \ell \in \mathbb{N}$.
