  Experimentally, jet physics studies face an unavoidable task: distinguishing,
at the detector level, the particles produced in the hard partonic scattering
from the ones created in unrelated soft processes such as pileup interactions
in high-luminosity proton-proton scattering or the underlying event in
heavy-ion collisions. The fluctuating nature of the background constitutes the
main source of uncertainty for any subtraction algorithm. Aiming at mitigating
the effect of such fluctuations, we present a new method to estimate the
background contribution to the transverse momentum on a jet-by-jet basis. Our
approach is based on estimating the median background momentum density stored
above a $p_{\rm T}$-cut applied at the constituent level and an experimentally
accessible correction term related to the signal contribution below the cut.
This allows to trade part of the uncertainty due to background contamination
for that of the signal below the cut, similarly to SoftKiller method. We
propose to reduce the fluctuations of the latter by exploiting intrinsic
correlations among the soft and hard sectors of QCD jets. Our data-driven
approach is tested against PYTHIA8 and JEWEL di-jet events embedded in a
thermal background and compared to the area-median and SoftKiller methods. The
main result of this study is a $\sim 5\!-\!40\%$ improvement on the resolution
of the reconstructed jet $p_T$ compared to previous methods in a
high-luminosity proton-proton scenario. Its applicability in a heavy-ion
context is also discussed.
