UNAUTH TKOF RWY ENTRY OP BY PVT PLT IN A CESSNA.

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IT WAS A BUSY AFTERNOON AT ICT. THERE WAS A LOT OF RADIO COM AT THE TIME OF THE OCCURRENCE. I WAS IN ACFT X SOLO; AT RWY 1R; INTXN B; COMPLETING THE BEFORE TKOF CHKLIST. UPON COMPLETION; I WAITED A MIN OR SO FOR A BREAK IN THE RADIO. WHEN I THOUGHT THE RADIO WAS CLR; I RPTED 'ICT TWR; CESSNA X; RWY 1R; INTXN B; READY FOR TKOF.' IMMEDIATELY AFTER THE CALL; THE TWR CAME BACK AND STATED 'CLRED FOR TKOF.' BECAUSE OF THE RESPONSE RETURNED IMMEDIATELY AFTER MY INITIAL CALL; AND NOT REALIZING AT THE TIME THAT MY TAIL NUMBER WAS NOT STATED; I IMMEDIATELY TAXIED ONTO THE RWY AND INITIATED MY TKOF. JUST BEFORE I PULLED ONTO THE RWY; I SCANNED DOWN THE LENGTH OF IT TO ENSURE IT WAS CLR. I DID SEE ANOTHER ACFT WHICH I BELIEVED TO BE TAXIING OFF THE RWY. I CONTINUED MY PROMPT DEP; AND JUST AFTER BECOMING AIRBORNE; I HEARD THE OTHER ACFT RPT 'TKOF ABORTED.' I CONTINUED THE TKOF TO CLR OUT OF THE WAY AND PROCEEDED TO THE W PRACTICE AREA WITH ATC PERMISSION. ATC INSTRUCTED ME TO CALL THE TWR UPON RETURN. SHORTLY AFTER TKOF I RETURNED FROM THE W PRACTICE AREA AND RETURNED HOME. I CONTACTED ICT TWR FROM THERE. I EXPLAINED TO THE TWR WHAT THE CONFUSION WAS AND DEEPLY AND REGRETFULLY APOLOGIZED FOR MY DEV. I FELT RUSHED AT THE TIME WHICH WAS PART OF MY MISTAKE. I BELIEVE WHAT HAPPENED WAS THAT WHEN I MADE MY INITIAL CALL; THE TWR INITIATED A CALL TO ANOTHER ACFT CLRING THEM FOR TKOF AND I ONLY CAUGHT THE TAIL END OF IT; 'RWY 1R; CLR FOR TKOF; MAKE IMMEDIATE DEP TO THE L.' I BELIEVE THAT BOTH MYSELF AND THE TWR WERE COMMUNICATING AT THE SAME TIME WHICH PROHIBITED ME FROM HEARING THE CALL SIGN. BELIEVING THAT THE CLRNC WAS MINE; I RESPONDED; 'CESSNA X CLRED FOR TKOF;' WHICH MAY HAVE ALSO BEEN COVERED PARTIALLY BY AN ATC XMISSION. I BELIEVE WE BOTH TAXIED ON AND INITIATED TKOF AT APPROX THE SAME TIME.