Wavelet quantile normalization (WQN) is a nonparametric algorithm designed to efficiently remove transient artifacts from single-channel EEG in real-time clinical monitoring. Today, EEG monitoring machines suspend their output when artifacts in the signal are detected. Removing unpredictable EEG artifacts would thus allow to improve the continuity of the monitoring. We analyze the WQN algorithm which consists in transporting wavelet coefficient distributions of an artifacted epoch into a reference, uncontaminated signal distribution. We show that the algorithm regularizes the signal. To confirm that the algorithm is well suited, we study the empirical distributions of the EEG and the artifacts wavelet coefficients. We compare the WQN algorithm to the classical wavelet thresholding methods and study their effect on the distribution of the wavelet coefficients. We show that the WQN algorithm preserves the distribution while the thresholding methods can cause alterations. Finally, we show how the spectrogram computed from an EEG signal can be cleaned using the WQN algorithm.