Abstract：
OBJECTIVE: Ultrafast Power Doppler (UPD) is a growing ultrasound modality for imaging and diagnosing microvasculature disease. A key element of UPD is using singular value decomposition (SVD) as a highly selective filter for tissue and electronic noise. However, two significant drawbacks of SVD are its computational burden and the complexity of its algorithms. These limitations hinder the development of fast and specific SVD algorithms for UPD imaging. This study introduces power SVD (pSVD), a simplified and accelerated algorithm for filtering tissue and noise in UPD images.
METHODS: pSVD exploits several mathematical properties of SVD specific to UPD images. In particular, pSVD allows the direct computation of blood-related SVD components from the temporal singular vectors. This feature simplifies the expression of SVD while significantly accelerating its computation. After detailing the theory behind pSVD, we evaluate its performances in several in vitro and in vivo experiments and compare it to SVD and randomized SVD (rSVD).
RESULTS: pSVD strongly decreases the running time of SVD (between 5 and 12 times in vivo) without impacting the quality of UPD images. Compared to rSVD, pSVD can be significantly faster (up to 3 times) or slightly slower but gives access to more estimators to isolate tissue subspaces.
CONCLUSIONS: pSVD is highly valuable for implementing UPD imaging in clinical ultrasound and provides a better understanding of SVD for ultrasound imaging in general.
METHODS: pSVD exploits several mathematical properties of SVD specific to UPD images. In particular, pSVD allows the direct computation of blood-related SVD components from the temporal singular vectors. This feature simplifies the expression of SVD while significantly accelerating its computation. After detailing the theory behind pSVD, we evaluate its performances in several in vitro and in vivo experiments and compare it to SVD and randomized SVD (rSVD).
RESULTS: pSVD strongly decreases the running time of SVD (between 5 and 12 times in vivo) without impacting the quality of UPD images. Compared to rSVD, pSVD can be significantly faster (up to 3 times) or slightly slower but gives access to more estimators to isolate tissue subspaces.
CONCLUSIONS: pSVD is highly valuable for implementing UPD imaging in clinical ultrasound and provides a better understanding of SVD for ultrasound imaging in general.
摘要：
目的：超快能量多普勒（UPD）是一种用于成像和诊断微血管疾病的不断发展的超声模式。UPD的关键要素是使用奇异值分解（SVD）作为组织和电子噪声的高度选择性滤波器。然而,SVD的两个重要缺点是它的计算负担和算法的复杂性。这些限制阻碍了用于UPD成像的快速和特定的SVD算法的发展。本研究引入了功率SVD(pSVD)，一种简化和加速的算法，用于过滤UPD图像中的组织和噪声。
方法：pSVD利用了特定于UPD图像的SVD的几个数学特性。特别是,pSVD允许从时间奇异向量直接计算血液相关SVD分量。此功能简化了SVD的表达，同时显着加速了其计算。在详细说明了pSVD背后的理论之后，我们在几个体外和体内实验中评估了其性能，并将其与SVD和随机SVD（rSVD）进行了比较。
结果：pSVD大大降低了SVD的运行时间（体内5至12倍），而不会影响UPD图像的质量。与rSVD相比，pSVD可以明显更快（最多3倍）或稍慢，但可以使用更多的估计器来分离组织子空间。
结论：pSVD对于在临床超声中实施UPD成像非常有价值，并且在总体上为超声成像提供了对SVD的更好理解。
方法：pSVD利用了特定于UPD图像的SVD的几个数学特性。特别是,pSVD允许从时间奇异向量直接计算血液相关SVD分量。此功能简化了SVD的表达，同时显着加速了其计算。在详细说明了pSVD背后的理论之后，我们在几个体外和体内实验中评估了其性能，并将其与SVD和随机SVD（rSVD）进行了比较。
结果：pSVD大大降低了SVD的运行时间（体内5至12倍），而不会影响UPD图像的质量。与rSVD相比，pSVD可以明显更快（最多3倍）或稍慢，但可以使用更多的估计器来分离组织子空间。
结论：pSVD对于在临床超声中实施UPD成像非常有价值，并且在总体上为超声成像提供了对SVD的更好理解。
