Accelerated and memory-efficient clutter filtering toward online-compatible ultrasound localization microscopy via compressed-matrix randomized QRD.

Ultrasound localization microscopy (ULM) enables super-resolution visualization of cerebral microvasculature; however, its clinical translation is hindered by the substantial computational burden of singular value decomposition (SVD)-based clutter filtering. To address this issue, we propose Compressed-Matrix Randomized QR Decomposition (CM-rQRD) as an accelerated and memory-efficient filtering framework. By integrating a Compressed-Matrix strategy into rQRD-based methods, the computational complexity of the decomposition step is substantially reduced. Specifically, the proposed methods achieve the lowest theoretical complexity, providing a 7.7-fold acceleration over conventional SVD while reducing memory usage to 50-65% of baseline levels. Although Power Doppler (PD) imaging exhibits a marginal 1-2 dB reduction in SNR and CNR, ULM reconstructions preserved spatial resolution and flow-related information comparable to SVDcov, with supplementary structural similarity values above 0.95. Furthermore, on an 800-frame in vivo dataset, CM-rQRDs complete clutter filtering in 72 ms on a CPU and in 7.7 ms on a GPU, underscoring their potential as online-compatible clutter-filtering modules for scalable ULM processing.