C172 student and instructor report rejected takeoff after conflict with helicopter; when pilot apparently accepted their takeoff clearance on an intersecting runway.

Narrative

I was about to take off for an IFR training flight with my instructor. After run-up; I contacted Tower for clearance to depart IFR. I received clearance to take off on Runway X. After responding to ATC; I proceeded to roll onto the runway. Once on centerline; I throttled up and started my takeoff roll. As takeoff roll started; I checked my airspeed indicator and called out 'airspeed alive.' After a few seconds of looking straight down the runway; I checked my engine gauges to ensure proper oil pressure. That took about 1 second. When I looked back up; I saw the helicopter crossing the runway at about 90 FT high approximately 1;500-2;000 FT ahead of me; petty much where Runway YY intersects XX. I immediately pulled the throttle and started braking. I could hear the Tower telling the helicopter that they were not cleared to take off. The helicopter pilot said he was sorry after peeling off left and back. Tower called and told me it was my discretion what I wanted to do; so I chose to do a 180 degree turn and back-taxied to start over so I would have the entire length of runway to work with again on takeoff. I believe the other pilot heard my takeoff clearance and thought it was his. I did have plenty of time to take action...this time.