We study exactly the solvable noncommutative scalar quantum Geld models of (2n) or (2n + 1) dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B·θ =±I in field theoretic context means the full restoration of the maximal U(∞) gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n- dimensional exactly solvable noncommutative φ4 quantum field model closely related to the 1+1- dimensional Moyal/ matrix-valued nonlinear Schr(o)dinger (MNLS) equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.