It don't look like Illinos Jacquet. He was playing a Selmer most of his carrier and that's no Selmer on the clip. I have no idea. But the drummer look like a young Bo Diddley (rip)!?!?!
"Clip from the Film Noir classic D.O.A. featuring James Von Streeter on tenor sax. Unfortunately he is not on the sound track, his band's playing was replaced by studio musicians."