A sparse-enhanced scaled gradient reweighted least-squares framework for efficient clutter filtering in ultrasound microvascular imaging

Accurate separation of blood flow signals from tissue clutter is essential for high-sensitivity ultrasound microvascular imaging. Robust principal component analysis (RPCA)-based clutter filtering has been widely investigated because it explicitly models ultrafast ultrasound data as the superposition of low-rank tissue and sparse blood flow components. Among these methods, iteratively reweighted least-squares RPCA (IRLS-RPCA) has shown strong modeling capability, but its closed-form alternating updates lack explicit step-size control and may slow convergence in challenging ultrasound imaging scenarios. In this work, we propose Sparse ScaledGD-IRLS, an efficient RPCA-based clutter filtering method for ultrasound microvascular imaging. The method introduces a scaled gradient descent (ScaledGD)-based update strategy into IRLS-RPCA to control the update step explicitly and accelerate convergence, while preserving the low-rank and sparse modeling capability. A plug-in sparse enhancement module is further incorporated to suppress residual background noise and improve image quality. The proposed method was validated using simulations, in vivo contrast-free human spinal cord data, and in vivo contrast-enhanced rat spinal cord ultrasound localization microscopy (ULM) data. Compared with representative clutter filters, Sparse ScaledGD-IRLS achieved better overall performance, including faster convergence, higher contrast-to-noise ratio and signal-to-noise ratio, improved spatial resolution, and clearer, more continuous vascular structures. Compared with IRLS-RPCA, it reduced the computational time by 53.8% in simulations and by 70.7% and 79.8% in the two human spinal cord datasets, respectively, while providing improved image quality; a similar trend was also observed in ULM. These results suggest that Sparse ScaledGD-IRLS improves the balance between image quality and computational efficiency.