I didn't know it, but I figured I could use some google-fu. Started by comparing the arcade version's music to the NES version. When I was sure they were the same enough that the original artist would get the credit even if someone else did the port, went on to look up who was credited with doing the arcade version's soundtrack. Came up with his alias "SCLAP". Then I went on to look for who SCLAP really was and came up with Masato Ishizaki. Searched for Masato Ishizaki to see what games he worked on to verify my work.
Though a very real possibility exists that Masahiko Ishida did Image Fight if I am interpreting my finds wrong.
Anyway, the last search came up with this interesting site:
http://vgmdb.net/artist/5333...