  Potential features in the primordial power spectrum, such as oscillatory
patterns, have been searched for in galaxy surveys in recent years, since these
features can assist in understanding the nature of inflation and distinguishing
between different scenarios 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
weakened or even wiped out on small scales in the late Universe due to
nonlinear 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
suite of large N-body simulations, we show that a recently-proposed nonlinear
reconstruction algorithm can effectively retrieve lost oscillatory features
from the mock galaxy catalogues and improve the accuracy of the measurement of
feature parameters (assuming such primordial features do exist). We do a Fisher
analysis to forecast how reconstruction affects the constraining power, and
find that it can lead to significantly more robust constraints on the
oscillation amplitude for a DESI-like survey. In particular, we compare the
application of reconstruction with other ways of improving constraints, such as
increasing the survey volume and range of scales, and show that it can achieve
what the latter do, but at a much lower cost.
