The magnetic resonance sounding (MRS) signal typically suffers from low signal-to-noise ratio (SNR). The MRS signal is severely distorted by noise, primarily harmonic and spiky noise. In terms of despiking, wavelet thresholding (WT) reconstructs the distorted content of the MRS signal, following isolation and elimination of the spiky sequence. However, WT cannot restore the MRS signal content completely when a series of spikes occurs within a given period of time. To solve this problem, a combined method of empirical mode decomposition (EMD) and WT for the removal of a series of spikes is proposed. EMD is first applied to decompose the noisy signal into several different components. The spikes that occur within a period of time are separated, the components without spikes are retained, and the components containing spiky events are selected and further processed by WT. After successively computing the wavelet coefficients of the selected components, the coefficients related to the spikes are isolated by threshold processing, and the subsequent wavelet reconstruction yields the sequence with the spikes removed. Finally, the denoised signal is obtained by adding the processed and retained components. The simulations on synthetic signals corrupted by artificial and real noise show that the proposed method improves the SNR with an accompanying improvement in the retrieval of the signal parameters. Moreover, the comparison results of the proposed and the WT methods suggest that the combined method efficiently removes a series of spikes.