IEEE Trans Ultrason Ferroelectr Freq Control. 2022 Aug;69(8):2425-2436. doi: 10.1109/TUFFC.2022.3180053. Epub 2022 Jul 29.
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.
有效去除组织杂波和噪声对于超快速多普勒成像是至关重要的。基于奇异向量分解（SVD）的时-空方法已被应用为一种经典方法来去除杂波和强运动伪影。然而，SVD 方法的性能通常取决于适当的特征向量阈值，即小值血流、大值静态组织和噪声的信号子空间的分离。在本研究中，通过基于 Cauchy 范数的稀疏惩罚，开发了一种基于 Cauchy 范数的鲁棒主成分分析（Cauchy-RPCA）方法，增强了小血管的血流提取。进一步采用随机空间下采样策略和增广拉格朗日乘子法（ADMM）来加速计算。对经典 SVD、传统 RPCA、基于盲反卷积的 RPCA（BD-RPCA）和提出的 Cauchy-RPCA 方法进行了面对面比较。使用从大鼠大脑记录的超快速超声成像数据集，研究了所提出的 Cauchy-RPCA 方法在杂波滤波、功率多普勒、彩色多普勒和功能超声（fUS）成像方面的性能。最后讨论了计算效率。
