  Potential features in the primordial power spectrum have been searched for in
galaxy surveys in recent years since these features can assist in understanding
the nature of inflation. The null detection to date suggests that any such
features should be fairly weak, and next-generation galaxy surveys, with their
unprecedented sizes and precisions, are in a position to place stronger
constraints than before. However, even if such primordial features once existed
in the early Universe, they would have been significantly damped in the
nonlinear regime at low redshift due to structure formation, which makes them
difficult to be directly detected in real observations. A potential way to
tackle this challenge for probing the features is to undo the cosmological
evolution, i.e., using reconstruction to obtain an approximate linear density
field. By employing a set of N-body simulations, here we show that a
recently-proposed nonlinear reconstruction algorithm can effectively retrieve
damped oscillatory features from halo catalogues and improve the accuracy of
the measurement of feature parameters (assuming that such primordial features
do exist). We do a Fisher analysis to forecast how nonlinear reconstruction
affects the constraining power, and find that it can lead to significantly more
robust constraints on the feature amplitude for a DESI-like survey. Comparing
nonlinear reconstruction with other ways of improving constraints, such as
increasing the survey volume and range of scales, this shows that it is
possible to achieve what the latter do, but at a lower cost.
