Randomized Spatial Downsampling-Based Cauchy-RPCA Clutter Filtering for High-Resolution Ultrafast Ultrasound Microvasculature Imaging and Functional Imaging

Effective tissue clutter filtering and noise removing are essential for ultrafast Doppler imaging. Singular vector decomposition (SVD)-based spatiotemporal method has been applied as a classical method to remove the clutter and strong motion artifacts. However, performance of the SVD-based methods often depends on a proper eigenvector thresholding, i.e., the separation of signal subspaces of small-value blood flow, large-value static tissue, and noise. In the study, a Cauchy-norm-based robust principal component analysis (Cauchy-RPCA) method is developed via Cauchy-norm-based sparsity penalization, which enhances the blood flow extraction of small-vessels. A randomized spatial downsampling strategy and alternating direction method of multipliers (ADMM) are further involved to accelerate the computation. A face-to-face comparison is carried out among the classical SVD, traditional RPCA, blind deconvolution-based RPCA (BD-RPCA), and the proposed Cauchy-RPCA methods. Ultrafast ultrasound imaging dataset recorded from rat brain is used to investigate the performance of the proposed Cauchy-RPCA method in terms of clutter filtering, power Doppler, color Doppler, and functional ultrasound (fUS) imaging. The computational efficiency is finally discussed.