Carter (back) was a full participant in Thursday's practice, Rich Cimini of ESPN.com reports.
A back injury prevented Carter from suiting up for the Jets' last two games, but he appears to be over the issue and he should return for Sunday's game against the Patriots, barring any setbacks. While Carter and starting corner D.J. Reed are trending towards playing Sunday, the Jets could be without top safeties Tony Adams (hamstring) and Ashtyn Davis (concussion), both of whom have missed the first two practices of the week.