Several strategies, known as clutter or wall Doppler filtering, were proposed to remove the strong echoes produced by stationary or slow moving tissue structures from the Doppler blood flow signal. In this study, the matching pursuit (MP) method is proposed to remove clutter components. The MP method decomposes the Doppler signal into wavelet atoms that are selected in a decreasing energy order. Thus, the high-energy clutter components are extracted first. In the present study, the pulsatile Doppler signal s(n) was simulated by a sum of random-phase sinusoids. Two types of high-amplitude clutter signals were then superimposed on s(n): time-varying low-frequency components, covering systole and early diastole, and short transient clutter signals, distributed within the whole cardiac cycle. The Doppler signals were modeled with the MP method and the most dominant atoms were subtracted from the time-domain signal s(n) until the signal-to-clutter (S/C) ratio reached a maximum. For the low-frequency clutter signal, the improvement in S/C ratio was 19.0 +/- 0.6 dB, and 72.0 +/- 4.5 atoms were required to reach this performance. For the transient clutter signal, ten atoms were required and the maximum improvement in S/C ratio was 5.5 +/- 0.5 dB. The performance of the MP method was also tested on real data recorded over the common carotid artery of a normal subject. Removing 15 atoms significantly improved the appearance of the Doppler sonogram contaminated with low-frequency clutter. Many more atoms (over 200) were required to remove transient clutter components. These results suggest the possibility of using this signal processing approach to implement clutter rejection filters on ultrasound commercial instruments.