The stochastic nature of cavitation implies visualization of the cavitation cloud in real-time and in a discriminative manner for the safe use of focused ultrasound therapy. This visualization is sometimes possible with standard echography, but it strongly depends on the quality of the scanner, and is hindered by difficulty in discriminating from highly reflecting tissue signals in different organs. A specific approach would then permit clear validation of the cavitation position and activity. Detecting signals from a specific source with high sensitivity is a major problem in ultrasound imaging. Based on plane or diverging wave sonications, ultrafast ultrasonic imaging dramatically increases temporal resolution, and the larger amount of acquired data permits increased sensitivity in Doppler imaging. Here, we investigate a spatiotemporal singular value decomposition of ultrafast radiofrequency data to discriminate bubble clouds from tissue based on their different spatiotemporal motion and echogenicity during histotripsy. We introduce an automation to determine the parameters of this filtering. This method clearly outperforms standard temporal filtering techniques with a bubble to tissue contrast of at least 20 dB in vitro in a moving phantom and in vivo in porcine liver.