noise abatement does not involve increasing thrust during rotation either. fine if you want to do something different, but please don’t suggest what you are doing relates to real life things like noise abatement. noise abatement in no way suggests using reduced thrust during take off and then increasing it upon rotation.
Take off thrust is set at the start of the roll. Normal take off profile is where the initial climb does not involve increasing speeds, you maintain V2 or V2+10 until acceleration height (typically 1000ft AAL), then you reduce pitch to allow the aircraft to accelerate to UP speed and retract flaps on schedule on the way.
with noise abatement you have an intermediate step where you reduce thrust (i.e. to reduce the noise) and reduce pitch but maintain speed (basically what is happening at 800-3000ft AGL on the diagram you posted), then at the delayed acceleration height you reduce pitch to accelerate the aircraft to UP speed and retract flaps on schedule.