In high-magnetic magnetic resonance imaging (MRI) systems (7 T and above), the radio frequency (RF) field shows greater inhomogeneity compared with clinical MRI systems (1.5 and 3.0 T). In multi-channel RF coils, driving each coil element with convex optimisation can reduce non-uniformity of the RF field in a region of interest. In this Letter, a periodic compressed method (PCM) and a PCM after averaging are proposed in order to reduce RF coil control time at high fields. Simulation results were obtained using a human head model in 7 and 9.4 T systems, and the results are discussed in detail.