We propose a new wavelet-based compressive sensing method to image coseismic radiation sources with teleseismic array data. Compared to the sliding-window-based technique, our method avoids choosing the window length by taking advantages of the adaptive resolution feature of the wavelet transform. Thus artefacts caused by inappropriate window length and waveform truncation can be removed. As waveforms usually become less aligned at late arrivals due to the increasing distance of actual radiation sources with respect to the hypocentre, we introduce a time-correction scheme to realign waveforms with the reference point obtained from beamforming at every time step. Synthetic tests indicate that the new method can better resolve the seismic radiation sources with more reliable locations and source times. To demonstrate its feasibility, we apply the method to the M_w 9.0 Tohoku earthquake. We find similar spatial rupture and seismic radiation patterns, such as repeating rupture in the region close to the hypocentre and along-dip frequency-dependent radiation, as indicated by previous models from finite-fault inversion and back projection. In addition, our results show structure-controlled rupture characteristics, with the seismic radiation in the first 80 s mainly confined in the off-Miyagi high-wave-speed region. The rupture speed shows clear along-dip variations, with updip rupture slower than that of downdip, which corresponds well with the depth-varying characteristics along the megathrust.