  The hard-scatter processes in hadronic collisions are often largely
contaminated with soft background coming from pileup in proton-proton
collisions, or underlying event in heavy-ion collisions. This paper presents a
new background subtraction method for jets and event observables (such as
missing transverse energy) which is based on the previously published
Constituent Subtraction algorithm. The new subtraction method, called Iterative
Constituent Subtraction, applies event-wide implementation of Constituent
Subtraction iteratively in order to fully equilibrate the background
subtraction across the entire event. Besides documenting the new method, we
provide guidelines for setting the free parameters of the subtraction
algorithm. Using particle-level simulation, we provide a comparison of
Iterative Constituent Subtraction with several existing methods from which we
conclude that the new method has a significant potential to improve the
background mitigation in both proton-proton and heavy-ion collisions.
