  In this study, we consider a variant of unlabelled sensing where the
measurements are sparsely permuted, and additionally, a few correspondences are
known. We present an estimator to solve for the unknown vector. We derive a
theoretical upper bound on the $\ell_2$ reconstruction error of the unknown
vector. Through numerical experiments, we demonstrate that the additional known
correspondences result in a significant improvement in the reconstruction
error. Additionally, we compare our estimator with the classical robust
regression estimator and we find that our method outperforms it on the
normalized reconstruction error metric by up to $20\%$ in the high permutation
regimes $(>30\%)$. Lastly, we showcase the practical utility of our framework
on a non-rigid motion estimation problem. We show that using a few manually
annotated points along point pairs with the key-point (SIFT-based) descriptor
pairs with unknown or incorrectly known correspondences can improve motion
estimation.
