(A,B) 2D and 1D excitation profiles of the non-accelerated transmission (i.e., reduction rate of 1); (C,D) 2D and 1D excitation profiles of the sparse parallel transmission at the reduction rate of 2 using proposed randomly perturbed spiral trajectory; (E,F) 2D and 1D excitation profiles of an RF pulse on regular spiral k-space trajectory for comparison purpose. The passband error of the regular spiral RF pulse was in the region of 0.3, which was worse than that of the proposed method (0.2).