Doppler ultrasound is a widely used technique for blood vessel detection and measurement. One important preprocessing procedure in Doppler ultrasound systems is the suppression of thermal noise and tissue clutter. This is typically done using high-pass filters. However, such filters have limited performance when the blood signals and tissue clutter have overlapping spectra. Recently, spatio-temporal filters based on singular value decomposition (SVD)have been proposed as an alternative, but they still suffer from tissue motion and thermal noise. In this work, we propose and demonstrate a novel technique for the removal of thermal noise, tissue clutter, and tissue motion artifact. The technique is based on principal component pursuit (PCP), which alternates low-rank approximations of the blood signals and projects the signals onto the ℓ 1 -norm ball. We also present the characterization of the performance of the PCP technique in simulation and phantom experiments, which shows substantial improvement in noise and clutter suppression. Compared to conventional filters, power Doppler images produced from signals filtered with PCP resulted in an improvement in SNR as high as 11 dB.