Multi‑stage singular value decomposition for ultrafast ultrasound imaging of microbubbles

Microbubble contrast-enhanced ultrasound (CEUS) relies on discriminating nonlinear bubble signals from linear tissue backscattering. While Singular Value Decomposition (SVD) filtering improves this discrimination, existing techniques often fail to retain the slowly-moving microbubble signals from static clutter. Here, we present a novel multi-stage singular value decomposition (MS-SVD) framework for ultrafast CEUS imaging. Our method employs plane-wave transmissions at multiple angles and acoustic pressure levels (implemented via duty-cycle modulation) and alternating transmit polarity. The beamformed data are then processed by three sequential SVD filters: (1) spatial-angular SVD to extract coherent signals across all transmit angles, (2) spatial-pressure SVD to separate linear fundamental and nonlinear harmonic components, and (3) spatiotemporal SVD to isolate moving microbubble echoes from tissue clutter. In in vitro flow phantoms and in vivo rat brain through a cranial window, MS-SVD dramatically improves microbubble detection compared to conventional SVD filtering, MS-SVD yields much stronger vascular contrast and suppresses tissue clutter to a greater extent. In the in vitro phantom, MS-SVD yielded 2.3-fold more ULM localizations and 1.8-fold more tracked trajectories, a 3.5 dB higher vessel-to-background contrast and a 40 % lower background localization density, giving denser and more complete super-resolution maps. By capturing the full acoustic signature of microbubbles (both fundamental and harmonic), MS-SVD achieves higher contrast-to-noise and sensitivity in CEUS. These gains make it a powerful front-end for super-resolution ultrasound localization microscopy and other high-sensitivity microvascular imaging applications.